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Geometry: Open Problems




Ten Geometry Problems
Visual Index
Problemas en Espanol (Spanishlanguage version)
Parallel lines
Perpendicular lines
Collinear Points
Triangle
Metric Relations
Quadrilateral
Triangle & Squares
Polygons
Pentagons
Hexagons
Heptagons
Octagons
Circle
Triangle
Centers Congruence
Similarity, Ratios, Proportions.


Geometry Problem 1426.
Post a solution
Two Squares, Collinear Points, Triangle, Quadrilateral, Sum of the Areas. 

Geometry Problem 1419.
Post a solution
Triangle, Altitude, Circumcircle, Incenter, Inradius, Perpendicular, Angle Bisector, Midpoint. 

Geometry Problem 1418.
Post a solution
Triangle, Circumcircle, Incenter, Side, Sum of Segments, Tangent, Parallel, Angle. 

Geometry Problem 1417.
Post a solution
Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles. 

Geometry Problem 1401.
Post a solution
Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. 

Geometry Problem 1400.
Post a solution
Triangle with three rectangles on the sides, Perpendicular Bisectors, Concurrency. 

Geometry Problem 1396.
Post a solution
Triangle with three rectangles on the sides, Vertices, Perpendicular lines, Concurrency. 

Geometry Problem 1395.
Post a solution
Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency. 

Geometry Problem 1394.
Post a solution
Three Circles and Three Pair of Common Internal Tangents, Concurrency. 

Geometry Problem 1385.
Post a solution
Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. 

Geometry Problem 1376.
Post a solution
Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines. 

Geometry Problem 1375.
Post a solution
Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base. 

Geometry Problem 1373.
Post a solution
Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base. 

Geometry Problem 1371: Equilic
Quadrilateral 5
Post a solution


Geometry Problem 1364.
Post a solution
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps. 

Geometry Problem 1361.
Post a solution
Triangle, Two NinePoint Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. 

Geometry Problem 1360.
Post a solution
Triangle, NinePoint Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. 

Geometry Problem 1359.
Post a solution
Triangle, Circumcircle, Congruent Angles, Midpoints. 

Geometry Problem 1351.
Post a solution Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. 

Geometry Problem 1345
Post a solution Three Equilateral Triangles, Center, Area, Common Vertex. 

Problem 1335. The
Lune of Hippocrates has the same area of a Kite.
Post a solution


Geometry Problem 1325.
Post a solution Octagons, Midpoints, Squares,
Mobile Apps, iPad. 

Geometry Problem 1320.
Post a solution Triangle, Incircle, Tangent, Chord, Circle, Parallel, Perpendicular, Collinearity. 

Geometry Problem 1319.
Post a solution Hexagons, Equilateral Triangles, Center, Midpoints. 

Geometry Problem 1317.
Post a solution Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence. 

Geometry Problem 1316.
Post a solution Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. 

Geometry Problem 1315.
Post a solution Triangle, Incircle, Tangent, Chord, Circle, Congruence. 

Static Diagram of problem 902
Dynamic Geometry Problem
902
Post a solution
Triangle, Four Squares, Center, Concurrent Lines.
GeoGebra, HTML5 Animation for Tablets


Geometry Problem 1301.
Post a solution Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. 

Geometry Problem 1282.
Post a solution
Three Squares, Common Vertex, Midpoint, Perpendicular, 90 Degrees. 

Geometry Problem 1253.
Post a solution Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency. 

Geometry Problem 1238
Post a solution Square, Equilateral Triangle, Metric Relations. Mobile Apps. 

Geometry Problem 1233
Post a solution Triangle, Euler Line, Orthic Axis, Perpendicular, 90 Degrees, Orthic Triangle. 

Geometry Problem 1212
Post a solution
Equilateral Triangle, Equilateral Hexagon, Concurrent Lines. 

Geometry Problem 1210
Post a solution
Circle, Tangent Line, Secant, Chord, Collinear Points. 

Geometry Problem 1176
Post a solution Cyclic Quadrilateral, Diagonals, Six Diameters, Circles, Collinear Points, Concurrent Lines. 

Geometry Problem 1175: Six Tangential or Circumscribed Quadrilaterals Theorem
Post a solution


Geometry Problem 1169
Post a solution Complete Quadrilateral, Orthocenters of the Component Triangles, Collinear Points, Ortholine, Steinerline, Orthocentric line. 

Geometry Problem 1168
Post a solution Construction of the Inscribed Circle of the Arbelos, Semicircles, Diameter, Circle, Triangle, Circumcircle, Tangent. 

Geometry Problem 1163.
Post a solution Isosceles Triangle, Congruence, Double Angle, Circle, Concyclic Points, Circumcenter, Perpendicular, Angle Bisector. 

Geometry Problem 1145.
Post a solution Three Squares, Midpoints. 

Geometry Problem 1143.
Post a solution Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points. 

Geometry Problem 1142.
Post a solution Cyclic Quadrilateral, Isogonal Lines, Circle, Center, Radius, Perpendicular Bisector, Circumcenter. 

Geometry Problem 1140.
Post a solution Triangle, Circumcircle, Circle, Center, Collinear Points. 
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Last updated: Mar 18, 2019






