Geometry Problems - Index (Page 1 of 40)

NCTM Processes: Problem Solving, Reasoning & Proof,
Communications, Connections, and Representation

Open Geometry Problems

Geometry Problem 881
Triangle, three Squares, Centers, Areas.

Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area.

Geometry Problem 879
Square, Midpoint, Diagonal, Ratio 3:1, Angle Measure.

Geometry Problem 878
Square, Inscribed Circle, Quadrant, Center, Perpendicular, Metric Relations.

Geometry Problem 877
Square, Right Triangle, Similarity, Metric Relations, Transversal.

Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas.

Geometry Problem 875
Congruent Circles, Intersecting Circles, Secant, Center, Angle Trisection, Triple Angle.

Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence.

Geometry Problem 873
Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence.

Geometry Problem 872
Quadrilateral, Triangle, Angle, 30, 90 degrees.

Geometry Problem 871
Brahmagupta's Theorem, Cyclic Quadrilateral, Perpendicular Diagonals, Midpoint.

Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint.

Geometry Problem 869
Triangle, Median, Three Equilateral Triangles, Collinear Points, Midpoint.

Geometry Problem 868
Cyclic Quadrilateral, Circle, Five Rectangles, Four Centers, Congruence.

Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence.

Geometry Problem 866
Cyclic Quadrilateral, Circle, Rectangle, Center, Congruence, 90 Degrees.

Geometry Problem 865
Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity.

Geometry Problem 864
Parallelogram, Diagonal, Congruence, Similarity, Metric Relations.

Geometry Problem 863
Circumscribed trapezoid, Inscribed Circle, Tangent, Metric Relations.

Geometry Problem 862:
Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square
.

Geometry Problem 861
Triangle, Incircle, Parallel, Tangent, Metric Relations.

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Geometry Problem 859
Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector.

Geometry Problem 858
Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines.

Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines.

Geometry Problem 856
Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 855
Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.

Geometry Problem 853
Square, Arc, Quadrant, Triangle, Perpendicular, Metric Relations.

Geometry Problem 852
Triangle, Incircle, Inradius, Tangent, Metric Relations.

Geometry Problem 851
Triangle, Triple side, Angles, 90 Degrees, Special Right triangle, Sides ratio 1:3.

Geometry Problem 850
Triangle, Double side, Angles, 90 Degrees, Special Right triangle.

Geometry Problem 849
Special Right triangle, Catheti or legs ratio 1:3, 18.5 Degrees. Double angle.

Geometry Problem 848
Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double angle.

Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points.

Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity.

Geometry Problem 845
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 844
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 843
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, Similarity.

Geometry Problem 842
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 841
Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence, Similarity.

Geometry Problem 840
Parallelogram, Perpendicular, Diagonal, Metric Relations, Similarity.

Geometry Problem 839
Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 838
Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 837
Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points.

Geometry Problem 836
Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations.

Geometry Problem 835
Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines.

Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional.

Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion.

Geometry Problem 832
Quadrilateral, Isosceles triangle, 70-70-40 degrees, Congruence, Auxiliary lines, Equilateral triangle.

Geometry Problem 831
Quadrilateral, Diagonal, Midpoint, Opposite Angles, Congruence, Parallelogram.

Geometry Problem 830
Quadrilateral, Triangle, Angles, 30 degrees, Congruence.

Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

Geometry Problem 828
Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian.

Geometry Problem 827: Brianchon Corollary
Circumscribed Hexagon, Tangency Points, Diagonal, Opposite Sides, Concurrent lines.

Geometry Problem 826: Brianchon's Theorem
Circumscribed Hexagon, Concurrent Diagonals.

Geometry Problem 825.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 824
Desargues' Theorem, Triangles in Perspective.

Geometry Problem 823.
Tangent Circles, Diameter, Perpendicular, Chord, Secant, Triangle, Area, Tangency Point.

Geometry Problem 822.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 821.
Adams Circle.

Geometry Problem 820.
Triangle, Cevian, Angles, 30 Degrees.

Geometry Problem 819.
Quadrilateral, Triangle, Angles, 30 degrees.

Geometry Problem 818.
Square, Triangle, Angle.

Geometry Problem 817.
Two circles, Tangent Lines, Circumscribed Quadrilaterals.

Geometry Problem 816.
Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Geometry Problem 815.
Triangle, Incircle, Semicircles, Arbelos, Area.

Geometry Problem 814.
Two Equilateral Triangles with a common Vertex, Angle.

Geometry Problem 813.
Right Triangle Area, Excircles, Cathetus, Tangency Points, Quadrilateral Area.

Geometry Problem 812.
Four Tangent Circles, Common Tangent Line, Diameter, Area, Collinear Centers.

Geometry Problem 811: Trisecting a line segment.
With four circles and one line.

Geometry Problem 810: Trisecting a line segment.
With two circles and eight lines.

Geometry Problem 809: Trisecting a line segment.
With three circles and four lines.

Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter.

Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area.

Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity.

Geometry Problem 805, Stewart Theorem
Triangle, sides and a cevian.

Geometry Problem 804
Butterfly theorem. Circle, Chord, Midpoints.

Geometry Problem 803
Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement.

Geometry Problem 802
Scalene Triangle, Median, Perpendicular, Angle, Measurement.

Geometry Problem 801
Equilateral Triangles, Cevian, Midpoint, Distance, Measurement, Metric Relations.

Geometry Problem 800
de Gua's Theorem, Pythagorean theorem in 3-D, Tetrahedron, Cubic Vertex, Triangular Pyramid, Apex, Height, Right Triangle Area, Base Area, Projected Area.

Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter.

Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle.

Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles.

Geometry Problem 796
Triangle, Altitude, Measurement of Angles.

Geometry Problem 795
Intersecting Circles, Common Chord, Midpoint, Tangent, Secant Line, Perpendicular, 90 Degrees.

Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence.

Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance.

Geometry Problem 792
Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles.

Geometry Problem 791
Regular Hexagon, Midpoints of Side and Diagonal, Equilateral Triangle, Area.

Geometry Problem 790
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line, Congruence.

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