Problem 1.
Triangle angles, median, congruence, isosceles, equilateral.

Problem 2.
Triangle and angles 80-80-20 degrees.

Problem 3.
Triangle, median and angles, 45 degrees.

Problem 4.
Quadrilateral, equal sides and angles 30-60, 120 degrees.

Problem 5. Triangle, cevian, equal segments, and angles, congruence.

Problem 6. Triangle, cevian, equal segments, and angles, congruence.

Problem 7. Triangle, cevian, equal segments, and angles, congruence.

Problem 8. Triangles, equal segments, and angles 45-45 degrees.

Problem 9. Triangles, equal segments, and angles.

Problem 10. Triangle, cevian, equal segments, and angles

Problem 11. Right triangle, cevian, and angles.

Problem 12. Triangle, cevian, equal segments, and angles.

Problem 13. Triangle, cevian, equal segments, and angles.

Problem 14.
Triangle, median, and angles

Problem 15.
Triangle, cevian, sum of segments, and angles.

Problem 16.
Triangle, cevian, perpendicular, and angles.

Problem 17.
Right triangle, altitude, and angles.
Problem 18.
Right triangle, cevian, and angles.

Problem 19.
Right triangle, perpendicular, and Excenter.

Problem 20.
Right triangle, altitude, incircles and inradii.

Problem 21.
Acute triangle, orthocenter, diameter, tangent.

Problem 22. Right triangle, altitudes, incircles and inradii.

Problem 23.
Right triangle, altitude, incircles and inradii.

Problem 24.
Right triangle, altitude, incircles and inradii

Problem 25.
Right triangle, altitude, incircles and inradius.

Problem 26.
Right triangle, altitude, incircles and inradius.

Problem 27.
Right Triangle, incircles and inradius

Problem 28.
Right Triangle, altitude, incircles and inradius.

Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.

Problem 29: Geometry Help.
Facts you should know.

Problem 30. Right Triangle, Incircle, Inradius.

Problem 31. Right Triangle, Incircle, Collinears.

Problem 32. Triangle, Cevian, Incircles, Tangents.

Problem 33. Triangle and quadrilateral.

Problem 34.
Right triangle, Cevian, Incircles, Tangents and Inradius

Problem 35.
Incenters and Inradii in Cyclic Quadrilateral.

Problem 36. Right triangle, altitude, incircles and inradii

Problem 37. Right triangle, altitude, incircles, incenters, and orthocenter.

Problem 38.
Right triangle, altitude, incircles, incenters, and angles.

Problem 39 Geometry Help. Facts you should know

Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.

Problem 40. Geometry Help.

Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.

Problem 41.
"Mickey Mouse." Three circles, tangents, radii.

Problem 42.
Angles, equal segments, and triangles.

Problem 43. Angles equal segments, and triangles

Problem 44.
Angles and triangles

Problem 45.
Angles and triangles.

Problem 46.
Triangle, median, and angles.

Problem 47.
Triangle, median, and angles.

Problem 48.
Angles and triangles.

Problem 49.
Right triangle, cevian, perpendicular, and angles

Problem 50.
Triangle with Equilateral triangles

Problem 51: Fagnano's Problem
Inscribed Triangle with the Minimum Perimeter.

Problem 52:
Angle bisector, circles.

Problem 53: 
Angle bisector, circles.

Problem 54.
Angle bisector, Circles, Midpoint of arc.

Problem 55:
Angle bisector, Circles, Cyclic Quadrilateral

Problem 56:
Angle bisector, Circles, Parallel Lines.

Problem 57:
Angle bisector, Circles, Cyclic Quadrilateral.

Problem 58:
Right Triangle, Congruence, Perpendiculars

Problem 59:
Right and Equilateral Triangles, Midpoints.

Problem 60: Isosceles triangle, congruence, equilateral.

Problem 61:
Trisection of Sides of a triangle, Menelaus theorem

Problem 62.
Square Diagonal, Inscribed Circle.

Problem 63. Regular Heptagon, side and diagonals, Ptolemy theorem

Problem 64:
Triangle, Incircle, Transversal, Menelaus theorem.

Problem 65:
Right Triangle, Midpoints.

Problem 66:
Triangle, Excircle, Tangents, Geometric Mean, Similarity.

Problem 67:
Triangle, Circumcircle, Angles, Cyclic Quadrilateral.

Problem 68:
Triangle, Incircle, Inradius, Tangent, Similarity

Problem 69: Square inscribed in a triangle, Similarity.

Problem 70:
Square inscribed in a triangle, Similarity.

Problem 71.
Cyclic Quadrilateral, Inscribed angle.

Problem 72. Intersecting Circles, Chords, Parallel.

Problem 73.
Three Intersecting Circles. Cyclic quadrilateral.

Problem 74.
Three Intersecting Circles. Cyclic quadrilateral.

Problem 75.
Three Intersecting Circles. Cyclic quadrilateral.

Problem 76. Area of a circle, square, circular sector.

Problem 77.
Circle, Parallel lines, Cyclic quadrilateral.

Problem 78:
Circle, Perpendicular and parallel lines, Midpoint, Cyclic quadrilateral, Congruence.

Problem 79:
Similar triangle.

Problem 80:
Area of triangle, side, incircle, inradius.

Problem 81:
Area of triangle, side, inradius, circumradius.

Problem 82:
Area of the Contact Triangle, inradius, circumradius.

Problem 83.
Area of the Excircle Contact Triangle, exradius, circumradius.

Problem 84.
Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.

Problem 85.
Contact Triangles Areas, Incircle, Excircle.

Problem 86.
Intouch and Extouch Triangles, Areas.

Problem 87.
Area of Quadrilaterals and Midpoints of Diagonals.

Problem 88.
Triangle and Quadrilateral Areas, Midpoints.

Problem 89.
Triangle Areas, Midpoints.

Problem 90.
Quadrilateral and Triangle Areas, Midpoints.

Problem 91.
Similar Triangles, Altitude, Parallel.

Problem 92.
Similar Triangles, Circumcircles, Circumradii, Parallel.

Problem 93.
Similar Triangles, Circumcircles, Parallelogram.

Problem 94.
Similar Triangles, Circumcircles, Circumradii.

Problem 95.
Similar Triangles, Inradii, Parallel.

Problem 96.
Similar Triangles, Incenters, Parallelogram.

Problem 97.
Similar Triangles, Areas.

Problem 98.
Quadrilateral Area, Centroid, Similarity.

Problem 99:
Circle Area, General Extension to Pythagoras' Theorem.

Problem 100.
Circle Area, Archimedes' Book of Lemmas

Problem 101.
Equilateral Triangle, Interior Point, Pythagorean Theorem, Angles.

Problem 102 .
Equilateral Triangle Area, Interior Point.

Problem 103.
Equilateral Triangle Area, Interior Point, Heron's Formula.

Problem 104.
Angles, Triangle.

Problem 105.
Angles, Triangle. Interior Point.

Problem 106.
Angles, Triangle. Cevian.

Problem 107.
Angles, Triangle. Cevian.

Problem 108.
Angles, Triangle, Median.

Problem 109.
Angles, Right Triangle, Cevian.

Problem 110.
Area of Contact Triangle.

Problem 111.
Orthogonal Circles.

Problem 112.
Area of square and triangle.

Problem 113.
Area of triangle, incircle, excircle.

Problem 114.
Area of triangle, incircle, excircle.

Problem 115 .
Area of triangle, excircles, tangent.

Problem 116.
Area of triangle, excircles, tangent.

Problem 117.
Area of triangle, incenter, excircles, tangent.

Problem 118.
Area of triangle, incenter, excenter, tangent

Problem 119 .
Area of triangle, incenter, excircle, tangent.

Problem 120 .
Area of triangle, incenter, excircles, tangent.


Problem 121.
Similarity and Area of triangle, Trisection of Sides.

Problem 122.
Marion Walter's Theorem. Area of triangle and Hexagon, Trisection of Sides.

Problem 123.
Area of triangle, Similarity, Trisection of Sides.

Problem 124.
Area of triangle, Similarity, Trisection of Sides.

Problem 125.
Area of Triangle, Star, Trisection of Sides. 

Problem 126.
Incenter of a Triangle, Angle Bisector, Proportions.

Problem 127.
Centroid and Incenter of a Triangle, Parallel, Proportions.

Problem 128.
Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

Problem 129.
Triangle, Concurrent Cevians, Sum of Ratios.

Problem 130.
Triangle, Concurrent Cevians, Sum of Ratios.


Problem 131.
Van Aubel Theorem, Concurrent Cevians, Sum of Ratios.

Problem 132.
Triangle, 60 degree, Orthocenter, Congruence, Midpoint

Problem 133.
Triangle, Angle Bisectors, Collinear Points.

Problem 134.
Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.

Problem 135.
Orthic Triangle, Altitudes, Perpendicular, Parallel.

Problem 136.
Orthic Triangle, Altitudes, Perpendicular, Concyclic Points.

Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.

Problem 138.
Nagel's Theorem, Orthic Triangle, Altitudes, Circumradius, Perpendicular.

Problem 139.
Triangle Area, Orthic Triangle, Semiperimeter, Circumradius.

Problem 140.
Triangle, Excircle, Tangent, Semiperimeter.
 

Problem 141.
Triangle, Incircle, Tangent , Parallel, Perimeters.

Problem 142.
Four Triangles, Incircle, Tangent and Parallel to Side, Areas.

Problem 143.
Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.

Problem 144.
Four Triangles, Incircle, Tangent and Parallel to Side, Inradii.

Problem 145.
Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.

Problem 146.
Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter.

Problem 147.
Quadrilateral, Area, Midpoints, Triangle.

Problem 148. Quadrilateral, Area, Midpoints.

Problem 149.
Quadrilateral, Area, Midpoints.

Problem 150.
Quadrilateral, Area, Trisection of Sides.

Problem 151.
Quadrilateral, Area, Trisection of Sides.

Problem 152.
Circumscribed Quadrilateral, Diagonal, Chord, Proportion.

Problem 153.
Circumscribed Quadrilateral, Diagonals Concurrent with Chords.

Problem 154.
Triangle, Inradius, Circumradius, Chord.

Problem 155.
Euler's Theorem Distance from the Incenter to the Circumcenter

Problem 156.
Triangle, Circumradius, Exradius, Chord, Secant line.

Problem 157.
Distance from the Circumcenter to the Excenter.

Problem 158.
Relation between the Circumradius, Inradius and Exradii of a triangle.

Problem 159.
Distances from the Circumcenter to the Incenter and the Excenters.

Problem 160.
Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.

Problem 161.
Parallelogram, Midpoints, Octagon, Areas.

Problem 162.
Parallelogram, Triangles, Areas.

Problem 163.
Trapezoid, Diagonals, Triangles, Areas.

Problem 164.
Parallelogram, Trapezoid, Diagonal, Triangles, Areas.

Problem 165. 
Parallelogram, Diagonal, Triangles, Areas.

Problem 166.
Parallelogram, Diagonal, Triangles, Areas.

Problem 167.
Parallelogram, Diagonal, Triangles, Areas.

Problem 168.
Parallelogram, Diagonal, Triangles, Pentagon, Areas.

Problem 169.
Parallelogram, Interior and Exterior Points, Diagonals, Pentagon, Triangles, Areas

Problem 170.
Trapezoid, Midpoint, Triangle, Area.

Problem 171.
Trapezoid, Midpoints, Triangles, Areas.

Problem 172.
Trapezoid, Midpoints, Quadrilaterals, Areas.

Problem 173.
Quadrilateral with Midpoints, Triangles, Areas.

Problem 174.
Quadrilateral with Midpoints, Triangles, Areas.

Problem 175.
Quadrilateral with Midpoints, Areas.

Problem 176.
Quadrilateral with Midpoints, Triangles, Areas

Problem 177.
Parallelogram with Midpoints, Triangles, Areas

Problem 178.
Quadrilateral, Trisection of sides, Area.

Problem 179.
Rhombus, Square, Diagonal, Angle.

Problem 180.
Circles Tangent Externally, Common External Tangents, Areas.

Problem 181.
Circular Sector of 90 degrees, find an angle.

Problem 182. Overlapping Circles, Find an angle.

Problem 183.
Right Triangle, Hypotenuse Trisection Points, Squares of the Distances.

Problem 184.
Triangle and Angles.

Problem 185.
Trapezoid, Triangles and Angles

Problem 186.
Right Triangle, Altitude, Incenters, Circles.

Problem 187.
Right Triangle, Altitude, Incenters, Circles, Angles.

Problem 188.
Square, Diagonal, 45 Degrees Angle.

Problem 189. Squares, Distances.

Problem 190.
Tangent circles, Tangent chord, Perpendicular, Distance.

Problem 191.
Triangle, Altitudes, Orthocenter, Squares, Areas.

Problem 192.
Circle, Diameter, Chord, Perpendicular, Triangle, Area.

Problem 193.
Area of a Triangle, Semiperimeter, Inradius.

Problem 194.
Area of a Triangle, Semiperimeter, Exradius.

Problem 195.
Area of a Triangle, Inradius, Exradii.

Problem 196.
Triangle, Inradius and Exradii Formula.

Problem 197.
Area of a Triangle, Side, Inradius, and Exradius.

Problem 198.
Triangle, Quadrilateral, Angles.

Problem 199.
Triangle, Quadrilateral, Angles.

Problem 200.
RightTriangle, Incircle, Excircles, Points of Tangency, Inradius.

Problem 201.
Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.

Problem 202.
Right Triangle, Incirle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.

Problem 203.
Right Triangle, Excircles, Exradii, Hypotenuse.

Problem 204.
Right Triangle, Incircle, Excircles, Inradius, Exradii.

Problem 205.
Right Triangle Area, Exradii relatives to legs or catheti.

Problem 206.
Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse.

Problem 207.
Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.

Problem 208.
Triangle, Excircles, Angles, 360 degrees.

Problem 209.
Triangle, Incircles, Inradius.

Problem 210.
Triangle, Angles, Auxiliary Lines.

Problem 211.
60 Degree Triangle, Equilateral triangles, Areas.

Problem 212.
120 Degree Triangle, Equilateral triangles, Areas.

Problem 213.
Triangle, Incircle, Inradius, Semicircles, Common Tangents.

Problem 214.
Quadrilateral and Angle Bisectors. 

Problem 215.
Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Problem 216.
Quadrilateral, Angle Bisectors, and Concurrency.

Problem 217.
Right triangle, Altitude and Projections.

Problem 218.
Right triangle, Altitude and Projections.

Problem 219.
Rhombus, Perpendiculars, Arithmetic Mean.

Problem 220.
Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Problem 221.
Viviani's theorem, Equilateral triangle, Interior point, Altitude, Distances.

Problem 222.
Viviani's theorem, Equilateral triangle, Exterior point, Altitude, Distances.

Problem 223.
Viviani's theorem, Isosceles triangle, Altitude, Distances.

Problem 224.
Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base.

Problem 225.
Viviani's Theorem Extension, Regular Polygon, Apothem, Distance.

Problemas Propuestos
de Geometria en Espanol.

Problem 226. Triangle, Centroid, Perpendicular lines.

Problem 227.
Triangle, Centroid, Exterior line, Perpendicular lines.

Problem 228.
Triangle, Midpoints, Exterior line, Perpendiculars lines.

Problem 229.
Triangle, Centroid, Transversal, Perpendicular lines.

Problem 230.
Triangle, Midpoints, Transversal, Perpendicular lines.

Problem 231.
Triangle, Midpoints, Transversal, Perpendicular lines.

Problem 232.
Parallelogram, Line through a vertex, Perpendicular lines.

Problem 233.
Parallelogram, Exterior line, Perpendicular lines.

Problem 234.
Parallelogram, Line through a vertex, Perpendicular lines.

Problem 235.
Parallelogram, Transversal line, Perpendicular lines.

Problem 236.
Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Problem 237.
Quadrilateral, Midpoints, Exterior line, Perpendicular lines.

Problem 238.
Square, Midpoints, Lines, Congruence.

Problem 239.
Square, Midpoints, Lines, Congruence, Pythagoras.
 
Problem 240.
Triangle with Equilateral triangles, Parallelogram.

Problem 241.
Triangle with Equilateral triangles, Congruence.

Problem 242.
Triangle with Equilateral triangles, Parallelogram.

Problem 243.
Triangle with Equilateral triangles, Parallelogram.

Problem 244.
Square, Diagonals, Centers, Distance.

Problem 245.
Parallelogram with Equilateral triangles.

Problem 246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon triangle.

Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Problem 249.
Triangle sides, medians, squares.
Problem 250.
Quadrilateral, sides, diagonals, midpoints, squares.

Problem 251.
Parallelogram, sides, diagonals, squares, areas.

Problem 252.
Rectangle, isosceles right triangle, square, area.

Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.

Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.

Problem 257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Problem 258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.

Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.

Problem 261.
Regular Pentagon inscribed in a circle, sum of distances.

Problem 262.
Regular Hexagon inscribed in a circle, sum of distances.

Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.

Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Problem 265.
Right Triangle, Pythagorean Theorem.

Problem 266.
Right Triangle, Altitude, Geometric Mean.

Problem 267. Right Triangle, Product of Catheti.

Problem 268.
Right Triangle, Catheti and Altitude.

Problem 269.
Right Triangle, Altitude, Perpendicular, Projection.

Problem 270.
Tangent Circles, Common external tangent, Fractional exponents.
 

Problem 271.
Tangent Circles, the Cube of the Common external tangent.

Problem 272.
Tangent Circles, the Cube of the Common external tangent.

Problem 273.
Triangle, Perpendiculars, Area of Squares.

Problem 274.
Isosceles Triangle, 80-80-20, Angles.

Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius.

Problem 276.
Square, 90 degree Arcs, Circle, Radius.

Problem 277.
Tangent Circles, Common External Tangent.

Problem 278.
Tangent Circles, Common External Tangent, Chord.

Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius.

Problem 280.
Quadrilateral, Perpendiculars, Area of Squares.

Problem 281.
Triangles, Angles, Isosceles, Equilateral.

Problem 282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence.

Problem 283.
Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius.

Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent, Radius.

Problem 285.
Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius.

Problem 286.
Square, Midpoints, Octagon.

Problem 287.
Regular Octagon, Diagonals.

Problem 288.
Tangent circles, Harmonic Mean, Radius, Diameter.

Problem 289.
Tangent circles, Radius, Perpendicular, Tangent.

Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent.

Problem 291.
Triangle, Circle, Circumradius, Perpendicular.

Problem 292.
Triangle, Parallel, Congruence, Similarity.

Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity.

Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse.

Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular

Problem 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular.

Problem 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular.

Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence

Problem 300.
Tangent to a circle, Secants, Square.

Problem 301.
Tangents to a circle, Secants, Square

Problem 302.
Triangle, Angle bisector of 60 degrees.

Problem 303.
Triangle, Angle bisector of 90 degrees.

Problem 304.
Triangle, Angle bisector of 120 degrees.

Problem 305.
Square, Triangles, Angles, Sides.

Problem 306.
Square, Triangles, Angles, Sides.

Problem 307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Problem 308.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Problem 309.
Regular Nonagon or Enneagon, Diagonals, Side.

Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle.

Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.

Problem 312.
Cyclic quadrilateral, Side extensions, Tangents.

Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Problem 314.
Tangent circles, Common external tangent line, Geometric Mean.

Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Problem 316.
Circular segments and Inscribed Squares.

Problem 317.
Right triangle and Inscribed Squares.

Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Problem 321.
Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity.

Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Problem 323.
Triangle, Incenter, Circumcenter, Equal circles, Collinearity.

Problem 324.
Quadrilateral with perpendicular diagonals, Concurrence.

Problem 325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle

Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Problem 327.
Right triangle Area, Incircle, Circumcircle, Square.

Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter. 

Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity.

Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent.

Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Problem 336.
Two equal circles, a Common Tangent and a Square. 

Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Problem 341.
Triangle, Inscribed circle, Tangent, Semiperimeter.

Problem 342.
Pentagon, Inscribed circle, Tangent, Semiperimeter.

Problem 343.
Hexagon, Inscribed circle, Tangent, Semiperimeter.

Problem 344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter.

Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Problem 346.
Equal circles, Tangents, Hexagon, Semiperimeter.

Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Problem 348.
Circles, Common External Tangents, Common Internal Tangent.

Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral. 

Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Problem 353.
Tangential quadrilateral, Diagonals, Incircles, Inradii.

Problem 354.
Rhombus, Square, 45 degrees.

Problem 355.
Circles, Common external tangent, Concyclic points.

Problem 356.
Square, Point inside, Triangles, Area.

Problem 357.
Square, Exterior point, Triangles, Area.

Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

Problem 362.
Circle, Chord, Perpendicular, Equal chords.

Problem 363.
Right triangle, Congruence, Angles.

Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence.

Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Problem 371.
Square, Inscribed circle, Triangle, Area

Problem 372.
Circles, Common Internal and External Tangent, Angles.

Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Problem 375.
Triangle, Excenter, External Angle Bisectors.

Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Problem 377.
Triangle, Internal Angle Bisector, Altitude. 

Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence. 

Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Angles.

Problem 382.
Concave Quadrilateral, Angle Bisectors, Angles.

Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Problem 390.
Triangle, Parallel lines, Collinear points.
 
Problem 391.
Triangle, Parallel lines, Collinear points.

Problem 392.
Triangle, Parallel lines, Concurrent lines.

Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Problem 395.
Square, 15 Degree, Equilateral triangle.

Problem 396.
Square, Angle Trisectors, Congruence, Area.

Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Problem 398.
Parallelogram, Area, Similarity, Congruence.
 

Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence.

Problem 407.
Circle, Angle, Tangent, Perpendicular, Secant, Radius, Center.

Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence.

Problem 410.
Two Regular Pentagons, Angle.

Problem 411.
Triangle, Median, Angles.

Problem 412.
Triangle, Angles, Congruence.

Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Problem 415.
Right Triangle, Cevian, Angles, Congruence.

Problem 416.
Triangle, Cevians, Trisectors, Area.

Problem 417.
Tangent circles, Tangent lines, Angles.

Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius.

Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Problem 421.
Right Triangle, Cevian, Angles, Measurement.

Problem 422.
Triangle, 24, 30 degree, Angle, Congruence.

Problem 423.
Triangle, 30, 40 degree, Angle, Congruence.

Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence.

Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence.

Problem 426.
Triangle, Circumradius, Circumcenter, concurrent Cevians.

Problem 427.
Triangle, Two Altitudes, Square of a Side.

Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement.

Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.

Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas.

Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal.

Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal.

Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity.

Problem 435.
Triangle, Incircle, Inradius, Congruent circles, tangent, Measurement.

Distance between the Incenter and the Centroid of a Triangle
Formula in terms of the sides a,b,c.

Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle.

Problem 440.
Triangle, Incircle, Incenter, Angle Bisector, Tangency Points, Circle, Angles.

Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Problem 442.
Triangle, Median, Cevian, Transversal, Congruent Angles.

Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles.

Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence.

Problem 445.
Three Tangent Circles, Tangency Points, Circumradius.

Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts.

Problem 447.
Complete Quadrilateral, Inradii, Exradii, Sides.

Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord.

Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord.

Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments.

Problem 451.
Triangle, Median, Congruence, Proportional Segments.

Problem 452.
Triangle, Circle, Tangent, Proportional Segments.

Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area.

Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius.

Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear.

Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius.

Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measure

Problem 459.
Right triangle, Squares, Distance, Measurement.

Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement.

Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement.

Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area.

Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees.

Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement.

Problem 466.
Concentric Circles, Secant, Congruence, Measurement.

Problem 467.
Concentric Circles, Chord, Tangent, Congruence, Measurement.

Problem 468.
Circle, Chord, Midpoint, Congruence, Angle.

Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence.

Problem 470.
Triangle, Parallel, Parallelogram, Area, Similarity.

Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity

Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity

Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

Problem 475.
Tangent Circles, Secant, Tangent, Parallel.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles.

Problem 477.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle.

Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion.

Problem 480.
Triangle, Circle, Center, Altitude, Angle, Circumcenter.

Problem 481.
Triangle, Altitude, Cevian, Perpendicular, Angle.

Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points.

Problem 483.
Square, Angle, 90 degrees, Measurement.

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence.

Problem 487.
Intersecting Circles, Area, Diameter, Parallel, 90 Degrees.

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle.

Problem 489.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area.

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel.

Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord.

Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel.

Problem 495.
Triangle, 120 Degrees, Angle Bisectors.

Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors.

Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees.

Problem 498.
Triangle, Angle Bisector, Double Angle, Measure.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure.

Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.

Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.

Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.

Problem 504.
Equilateral Triangle, Angles, 45, 60 Degrees.

Problem 505.
Right Triangle, Cevian, Sum of Segments, Angles.

Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.

Problem 507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle.

Problem 508.
Triangle with three Squares, Four triangle of equal Area.

Problem 509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map.

Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.

Problem 511.
Triangle, Double Angle, Angle Bisector, Measure.

Problem 512.
Triangle with three squares and concurrency.

Problem 513.
Triangle, Double Angle, Exterior Angle Bisector, Measure.

Problem 514.
Triangle, Five Squares, Line, Area.

Problem 515.
Triangle, Double Angle, Altitude, Measure.

Problem 516.
Triangle, Cevian, Congruence, Angles.

Problem 517.
Right Triangle, Six Squares, Areas.