Geometry Theorems and Problems  Recent Additions (Page
9 of 15)




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

Euclid's Elements Book I, Proposition 4: (SideAngleSide SAS) 

Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less 

Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line 

Euclid's Elements Book I, Proposition 1:
On a given finite line to construct an equilateral triangle 

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

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

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

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

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

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

Proposed
Problem 417.
Tangent circles, Tangent lines, Angles. 

Routh's Theorem  Index
Triangle, Cevians, Area, Ratio.


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. 

Proposed
Problem 416.
Triangle, Cevians, Trisectors, Area. 

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

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

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

Proposed
Problem 412.
Triangle, Angles, Congruence. 

Proposed
Problem 411.
Triangle, Median, Angles. 

Proposed
Problem 410.
Two Regular Pentagons, Angle. 

Proposed
Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence. 

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

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

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

Concurrent lines.
Theorems and Problems Index. 

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

Median of a Trapezoid, Theorems and Problems.
Index.


Circular
Sector.
Index.
Theorems and Problems.


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

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

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

Points, Theorems and Problems  Index. 

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

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

Proposed
Problem 398.
Parallelogram, Area, Similarity, Congruence. 

Proposed
Problem 397.
Triangle, Altitude, Midpoints, Congruence. 

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

Proposed
Problem 395.
Square, 15 Degree, Equilateral triangle. 

Kosnita's
Theorem.
Circumcenters, Concurrent lines. 

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

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

Median Index.
Theorems and Problems. 

Proposed
Problem 392.
Triangle, Parallel lines, Concurrent lines. 

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

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

Proposed
Problem 389.
Triangle, Parallel lines, Harmonic Mean. 

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

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

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

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

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

Proposed
Problem 383.
Concave
Quadrilateral, Angle Bisectors, Semidifference of Angles. 

Proposed
Problem 382.
Concave
Quadrilateral, Angle Bisectors, Angles. 

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

Chord.
Index.
A chord of a circle is the line segment joining two points on the
circle.


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

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

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

Proposed
Problem 377.
Triangle, Internal Angle Bisector, Altitude. 

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

Proposed
Problem 375.
Triangle, Excenter, External Angle Bisectors. 

Proposed
Problem 374.
Triangle, Incenter, Internal Angle Bisectors. 

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

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

Proposed
Problem 371.
Square, Inscribed circle, Triangle, Area. 

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

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

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

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

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

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

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

Special Right Triangle
3060.


Special Right Triangles.


Obtuse Triangle. 

Proposed
Problem 363.
Right triangle, Congruence, Angles. 

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

Euclid's Elements Book I Word Cloud.


Mascheroni
construction with compass alone. Index


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

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

Proposed
Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus. 

Mascheroni construction: Find the center of a circle with compass alone.


Proposed
Problem 358.
Isosceles triangle 808020, Circle, Angles, Congruence. 

Euclid's
Elements, Book X, Lemma for Proposition 33 One page visual illustration. 

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

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

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

Proposed
Problem 354.
Rhombus, Square, 45 degrees. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tangent Circles Index


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

Proposed Problem
335.
Cyclic Quadrilateral, Perpendiculars to Sides. 

Proposed Problem
334.
Cyclic Quadrilateral, Perpendiculars to Diagonals. 

Midpoints.
Theorems and Problems 

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

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

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

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

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

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

Tangential or Circumscribed Quadrilateral:
Diagonals, Altitudes Theorem. 

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

Proposed Problem
326.
Equilateral triangle, Semicircle, Equal arcs. 

Tangential or Circumscribed Quadrilateral:
Diagonals, Inradii Theorem. 

Tangential
or Circumscribed Quadrilateral


Six Tangential or Circumscribed Quadrilaterals Theorem. 

Tangential or Circumscribed Quadrilateral:
Pitot Theorem. 

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

Proposed Problem
324.
Quadrilateral with perpendicular diagonals, Concurrence. 

Altitude Index.
Theorems and Problems. 

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

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

Collinear Points. 

Incenter.
Index.


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

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

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

Proposed Problem
317.
Right triangle and Inscribed Squares. 

Proposed Problem
316.
Circular segments and Inscribed Squares. 

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

Polygons. 

Proposed Problem 287:
Regular Octagon. 

Octagons. 

Proposed Problem 286:
Square, Midpoints, Octagon. 

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

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

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

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