Geometry Theorems and Problems - Recent Additions (Page
8 of 15)
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Problem
549.
Parallel lines, Transversal, Angle Sums. |
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Problem
548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points,
Similarity. |
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Problem
547.
Triangle, Transversal, Four Circumcircles, Concurrency. |
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Circumcircle
Index.
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Problem
546.
Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle. |
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Problem
545.
Acute Triangle, Squares, Altitudes, Area, Measure. |
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Problem
544.
Right Triangle, Altitude, Median, Equal angles, Measure. |
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Geometry Problems
341 -
350.
Triangle, Quadrilateral, Pentagon, Hexagon, Inscribed circle, Tangent, Semiperimeter, Equal circles, Concurrent lines, Altitude, Concyclic Points, Cevian, Incircle. |
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Problem
543.
Right Triangle, Altitude, Angle Bisector, Median. |
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Problem
542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees. |
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Problem
541.
Right Triangle, Altitude, Angle Bisector, Congruence. |
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Geometry Problems
331 -
340.
Square, Circle, Similarity, Cyclic quadrilateral, Trapezoid, Triangle, Isosceles, Circumcircle, Incircle, Diagonal, Tangent, Perpendicular, Parallel, Concyclic points. |
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Geometry Problems
321 -
330.
Triangle, Square, Circle, Area, Cyclic quadrilateral, Tangent, Incenter, Circumcenter, Excircle, Midpoint, Altitude, Collinearity, Concurrence, Isosceles, Equilateral, Parallel, Perpendicular, Diameter, Concyclic. |
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Geometry Problems
311 -
320.
Circle, Semicircle, Chord, Diameter, Tangent, Cyclic quadrilateral, Geometric mean, Square, Right triangle, Altitude, Collinearity, Circumcircle, Incenter, Excenter. |
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Geometry Problems
301 -
310.
Circle, Tangent, Secant, Square, Triangle, Angle Bisector, 45, 60, 90, 120 Degrees, Side, Nonagon, Midpoint, Arc, Diagonal, Semicircle. |
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Geometry Problems 231 - 240.
Triangle, Quadrilateral, Square, Parallelogram, Trapezoid, Altitude, Distances, Midpoint, Perpendicular, Transversal. |
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Problem
540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
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Geometry Problems 291 -
300.
Triangle, Circle, Square, Congruence, Similarity, Circumradius, Perpendicular, Parallel, Secant, Tangent, Chord, Intersection, Midpoint, Radius, Angle. |
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Problem
539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
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Geometry Problems 281 -
290.
Triangle, Square, Circle, Octagon, Congruence, Isosceles, Equilateral, 90 Degrees, Circular Sector, Semicircle, Tangent, Radius, Diameter, Harmonic Mean. |
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Problem
538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint. |
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Problem
537.
Rectangle, Midpoints, Diagonal, Angle Bisector. |
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Problem
536.
Intersecting Circles, Chord, Perpendicular. |
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Problem
535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Center, Tangent,
Collinear. |
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Problem
534.
Right Triangle, Squares, Perpendicular, Dissection, Areas. |
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Geometry Problems 271 -
280.
Circle, Quadrilateral, Square, Tangent, Cube, Triangle, Isosceles, Area, 90-80-80-20 Degrees, Circumcircle, Sagitta, Inradius, Chord, Perpendicular. |
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Geometry Problems 261 -
270.
Regular Polygon, Pentagon, Hexagon, Circle, Tangent, Similarity, Triangle, Hypotenuse, Catheti, Geometric Mean, Altitude, Projection, Fractional Exponent. |
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Problem
533.
Euclid's
Elements, Book XIII, Proposition 10. One page visual illustration. |
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Geometry Problems 251 -
260.
Parallelogram, Rectangle, Triangle, Square, Circle, Area, Side, Equilateral, Isosceles, Centroid, Distance, Vertex, Circumcircle, Incircle, Tangent, Diagonal. |
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Brahmagupta Theorem and Problems - Index
Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral. |
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Solid Geometry: Morphing Platonic Solids. Sacred geometry, Video and News.
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Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area. |
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Ptolemy's Theorems and Problems - Index. |
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Semiperimeter, Perimeter Index.
Theorems and Problems. |
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Problem 531.
Triangle, Angle Bisector, Midpoint, Parallel, Perimeter, Semiperimeter. |
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Geometry Problems 241 - 250.
Triangle, Quadrilateral, Congruence, Area, Parallelogram, Square, Diagonal, Center, Napoleon, Median, Midpoint. |
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Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence. |
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Problem 529.
Right Trapezoid, Circle, Diameter. |
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Problem 528.
Triangle, Medians, Perpendicular, Measurement. |
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Problem 527.
Circle, Tangent, Secant, Chord, Midpoint, Measurement. |
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Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement. |
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Geometry Problems 221 - 230.
Isosceles, Equilateral triangle, Viviani's theorem, Altitude, Distances, Regular Polygon, Apothem, Centroid, Midpoint, Perpendicular, Transversal.. |
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Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement. |
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Problem 524.
Circle, Equilateral Triangles, Midpoint, Side, Measurement. |
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Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity. |
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Problem 522.
Right Triangle, Circle, Diameter, Tangent. |
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Problem
521.
Triangle with three Squares, Altitude, Rectangle, Area. |
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Geometry Problems
211 -
220.
Equilateral triangle, Quadrilateral, Area, Cyclic Quadrilateral, 60 Degree, Angle Bisector, 120, incircle, Inradius, Semicircle, Tangent, Concurrency, Right triangle, Altitude, Projection, Rhombus, Perpendicular, Arithmetic Mean, Distance. |
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Problem
520.
Triangle with six Squares, Ratio, Area. |
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Problem
519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area. |
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Geometry Problems 191 -
200.
Triangle, Circle, Square, Area, Circle, Diameter, Altitude, Orthocenter, Semiperimeter, Inradius, Exradius, Quadrilateral, Angle, Tangent, Right triangle. |
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Problem
518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure. |
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Problem
517.
Right Triangle, Six Squares, Areas. |
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Problem
516.
Triangle, Cevian, Congruence, Angles. |
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Problem
515.
Triangle, Double Angle, Altitude, Measure. |
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Geometry Problems 181 -
190.
Right Triangle, Trapezoid, Square, Intersecting Circles, Circular Sector, 90 Degrees, Angles, Trisection, Hypotenuse, Distance, Incenter, Altitude, Diagonal, 45 Degrees, Tangent, Chord, Perpendicular. |
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Problem
514.
Triangle, Five Squares, Line, Area. |
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Problem
513.
Triangle, Double Angle, Exterior Angle Bisector, Measure. |
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Geometry Problems 171 -
180.
Area, Triangle, Quadrilateral, Circle, Parallelogram, Trapezoid, Square, Rhombus, Diagonal, Angle, Tangent, Trisection. |
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Geometry Problems 161 -
170.
Area, Triangle, Parallelogram, Trapezoid, Pentagon, Diagonal, Midpoint, Octagon. |
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Problem
512.
Triangle with three squares and concurrency. |
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Problem
511.
Triangle, Double Angle, Angle Bisector, Measure. |
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Problem
510.
Triangle, Three Squares, Midpoints, Concurrency. |
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Problem
509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map. |
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Geometry Problems 151 -
160.
Triangle, Quadrilateral, Area, Trisection, Circle, Proportion, Diagonal, Chord,Inradius, Circumradius, Exradius, Euler, distance, Incenter, Circumcenter, Excenter, Incircle, Circumcircle. |
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Problem
508.
Triangle with three Squares, Four triangle of equal Area. |
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Problem
507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle. |
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Problem
506.
Triangle with Three Squares, Center, Midpoint, Perpendicular. |
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Problem
505.
Right Triangle, Cevian, Sum of Segments, Angles. |
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Problem
504.
Equilateral Triangle, Angles, 45, 60 Degrees. |
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Ten Geometry Problems, Visual Index |
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Problem
503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency. |
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Geometry Problems 141 -
150.
Triangle, Quadrilateral, Parallelogram, Incircle, Incenter, Tangent, Parallel, Perimeter, Area, Inradius, Circumradius, Midpoint, Varignon, Trisection. |
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Problem
502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure. |
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Problem
501.
Triangle, Two Squares, Center, Midpoint, another Square. |
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Problem
500.
Circle, Diameter, Chord, Perpendicular, Measure. |
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Problem 499.
Triangle, Two Squares, Perpendicular. |
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Problem 498.
Triangle, Angle Bisector, Double Angle, Measure. |
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Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees. |
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Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors. |
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Problem 495.
Triangle, 120 Degrees, Angle Bisectors. |
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Geometry Problems
121 -
130.
Triangle, Area, Similarity, Trisection, Hexagon, Star, Incenter, Centroid, Parallel, Proportions, Angle Bisector, Ratio |
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Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel. |
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Geometry Problems
111 -
120.
Orthogonal Circles, Triangle, Square, Area, Incircle, Excircle, Tangent, Incenter |
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The Simson Line,
Theorems and Problems - Index. |
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Geometry Problems
101 -
110.
Angle, Equilateral Triangle, Pythagorean Theorem, Median, Heron, Cevian, Contact Triangle. |
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Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord. |
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Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel. |
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Geometry Problems
91 -
100.
Similarity, Triangles, Altitude, Parallel, Circumcircle, Parallelogram, Incenter, Area, Centroid, Quadrilateral, Archimedes, Pythagoras. |
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Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius. |
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Geometry Problems
81 -
90.
Triangle, Quadrilateral, Circle, Incircle, Circumcircle, Excircle, Inradius, Circumradius, Exradius, Contact Triangle, Area, Midpoint. |
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Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area. |
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Problem 489.
Parallelogram, Triangle, Quadrilateral, Area. |
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Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle. |
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Geometry Problems
71 -
80.
Cyclic Quadrilateral, Intersecting Circles, Area, Inradius, Incircle. |
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Problem 487.
Intersecting
Circles, Area, Diameter, Parallel, 90 Degrees. |
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Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence. |
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Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement. |
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Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion. |
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Geometry Problems - Visual Index. |
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Problem 483.
Square, Angle, 90 degrees, Measurement. |
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Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points. |
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Problem 481.
Triangle, Altitude, Cevian, Perpendicular, Angle. |
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Geometry Problems
61 -
70.
Triangle, Quadrilateral, Circle, Cyclic, Similarity. |
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Problem 480.
Triangle, Circle, Center, Altitude, Angle, Circumcenter. |
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Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion. |
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Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle. |
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Problem 477.
Parallelogram, Triangle, Quadrilateral, Area. |
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Geometry Problems
51 -
60.
Triangle, Quadrilateral, Circle, Cyclic Quadrilateral. |
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Problem 476.
Triangle, Circumcenter, Circumcircle, Angles. |
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Problem 475.
Tangent Circles, Secant, Tangent, Parallel. |
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Geometry Problems
41 -
50.
Triangle, Sangaku, Quadrilateral, Circle, 30-60 Degrees. |
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Problem 474.
Parallelogram, Diagonal, Circle, Vertex. |
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Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
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Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
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Geometry Problems 21 -
30.
Right triangle, Altitude, Incircle and inradius, Congruence, Circle. |
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Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity. |
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Geometry Problems 11 -
20.
Angle, Angle bisector, Triangle, Altitude, Median, Congruence, Cevian, Circle,
Excircle, Excenter, Inradius, Exradius |
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Problem 470.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
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Geometry Problems 1 - 10.
Angle, Triangle, Quadrilateral, Congruence, 20, 30, 45, 60, 80, 120 degrees,
Median, Auxiliary lines. |
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Proposed
Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence. |
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Proposed
Problem 468.
Circle, Chord, Midpoint, Congruence, Angle. |
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Proposed
Problem 467.
Concentric Circles, Chord, Tangent, Congruence, Measurement. |
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Proposed
Problem 466.
Concentric Circles, Secant, Congruence, Measurement. |
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Proposed
Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement. |
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Napoleon's theorems and problems, Index. |
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Proposed
Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees. |
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Concentric
Circles.
Index.
Theorems and Problems.
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Concentric
Circles Definition. |
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Proposed
Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area. |
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Proposed
Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement. |
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Proposed
Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement. |
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Proposed
Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement. |
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Proposed
Problem 459.
Right triangle, Squares, Distance, Measurement. |
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Proposed
Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement. |
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Proposed
Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius. |
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Proposed
Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear. |
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Proposed
Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees. |
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Proposed
Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius. |
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Proposed
Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area. |
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Triangle Centers,
Visual Index. |
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Fermat Point.
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Vecten
Outer Point.
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Proposed
Problem 452.
Triangle, Circle, Tangent, Proportional Segments. |
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Proposed
Problem 451.
Triangle, Median, Congruence, Proportional Segments. |
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Proposed
Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments. |
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Proposed
Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord. |
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Proposed
Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord. |
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Proposed
Problem 447.
Complete Quadrilateral, Inradii, Exradii, Sides. |
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Complete Quadrilateral Index.
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Proposed
Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts. |
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Proposed
Problem 445.
Three Tangent Circles, Tangency Points, Circumradius. |
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Proposed
Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence. |
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Proposed
Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles. |
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Proposed
Problem 442.
Triangle, Median, Cevian, Transversal, Congruent Angles. |
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Proposed
Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
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Proposed
Problem 440.
Triangle, Incircle, Incenter, Angle Bisector, Tangency Points, Circle, Angles. |
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Marion Walter's Theorem
and Related Topics: Index |
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Proposed
Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle. |
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Proposed
Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement,
Parallel lines. |
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Proposed
Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. |
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Proposed
Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. |
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Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c. |
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Distances between Triangle Centers
Index.
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Proposed
Problem 435.
Triangle, Incircle, Inradius, Congruent circles, tangent, Measurement. |
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Proposed
Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity. |
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Proposed
Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
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Proposed
Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal. |
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Proposed
Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal. |
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Transversal Lines. |
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Proposed
Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas. |
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Obtuse Angle.
Theorems and Problems. |
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Isosceles Triangle
80-20-80. Index |
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Proposed
Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement. |
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Proposed
Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement. |
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Euclid's Elements Book I, Proposition
8: (Side-Side-Side SSS Congruence) |
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Euclid's Elements Book I, Proposition
7
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point,... |
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Proposed
Problem 427.
Triangle, Two Altitudes, Square of a Side. |
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Proposed
Problem 426.
Triangle, Circumradius, Circumcenter, concurrent Cevians. |
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Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles |
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Area
of a Square Index.
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Euclid's Elements Book I, Proposition
6: Converse of I.5 |
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Proposed
Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence. |
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