GoGeometry: Open Problems, High School, College

Open Geometry Problems - Index

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

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

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

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

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

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

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

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

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

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

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

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

Geometry Problem 772
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Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations.

Geometry Problem 744.
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Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations.

Geometry Problem 738.
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Intersecting Circles, External Common Tangent, Common Chord, Secant, Circumcircle, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 733.
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Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency.

Geometry Problem 732.
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Triangle, Altitude, Orthic Triangle, Orthocenter, Congruence, Parallelogram.

Geometry Problem 724.
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Circumscribed Quadrilateral, Circle, Angle, Incenter, Half the Measure.

Geometry Problem 721.
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Triangle, Orthocenter, Circumcircle, Altitude, Collinear points.

Geometry Problem 715.
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Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

Problem 690: Distance between the Incenter and the Centroid of a Triangle.
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Formula in terms of the sides a,b,c.

Geometry Problem 689.
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Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.

Geometry Problem 688.
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Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya.

Geometry Problem 675.
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Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points.

Geometry Problem 674.
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Triangle, Altitude, Angles.

Geometry Problem 658.
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Triangle, Altitudes, Diameter, Circle, Angles.

Geometry Problem 656.
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Triangle, Cevian, Concurrent Lines.

Geometry Problem 638
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Arbelos and Inscribed Circle: Concyclic Points.

Geometry Problem 633
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Triangle, Parallel Lines, Intersecting Lines.

Geometry Problem 632.
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Triangle, Interior and Exterior Angle Bisectors, Midpoints, Collinear Points.

Geometry Problem 629
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Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Geometry Problem 612
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Altitude of a Triangle, Perpendicular, Congruence.

Geometry Problem 611
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Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Geometry Problem 610
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Intersecting Circles, Radius, Parallel, Common Tangent, Angle, 90 Degrees.

Geometry Problem 609
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Triangle, Perpendiculars, 90 Degrees, Collinearity.

Geometry Problem 608
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Square with Right Triangles, Metric Relations, Congruence, Measurement.

Geometry Problem 607
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Intersecting Circles, Triangles, Metric Relations, Measurement.

Geometry Problem 600
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Circle, Area, Tangent, Semicircle, Tangency Point.

Geometry Problem 596
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Quadrilateral, Right Triangle, Isosceles, Midpoint.

Geometry Problem 586
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Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

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

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

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

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