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Geometry: Open Problems, High School, College, Tutoring

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Geometry: Open Problems

Dynamic Geometry 1481

Dynamic Geometry 1481.
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Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1480

Dynamic Geometry 1480.
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Japanese Theorem for Cyclic Polygon, Sangaku,  Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1478

Dynamic Geometry 1478.
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Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1477

Dynamic Geometry 1477.
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Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1476

Dynamic Geometry 1476.
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Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1475

Dynamic Geometry 1475.
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Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad.

Dynamic Geometry 1473

Dynamic Geometry 1473.
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Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration.

Dynamic Geometry 1471

Dynamic Geometry 1471.
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Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration.

Dynamic Geometry 1470

Dynamic Geometry 1470.
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Tangential Quadrilateral, Incircles, Tangent, Parallel, Rhombus, Step-by-step Illustration.

Geometry Problem 1466

Geometry Problem 1466.
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Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points. Step-by-step Illustration using GeoGebra.

Geometry Problem 1461

Geometry Problem 1462.
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Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals, Collinear Points.

Geometry Problem 1460

Dynamic Geometry 1460.
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Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals, Collinear Points, Step-by-step Illustration using GeoGebra.

Geometry Problem 1459

Geometry Problem 1459.
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Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra.

Geometry Problem 1458

Geometry Problem 1458.
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Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra.

Geometry Problem 1457

Geometry Problem 1457.
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Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1455

Geometry Problem 1455.
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Nagel Point, Excircles, Incircle, Congruent Segments, iPad. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1451

Dynamic Geometry 1451.
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Orthopole of a Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1450

Dynamic Geometry 1450.
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Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1449

Dynamic Geometry 1449.
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Salmon Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1448

Dynamic Geometry 1448.
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Simson Line. Step-by-step illustration using GeoGebra.

Problem 1444

Dynamic Geometry Problem 1444.
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The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra.

Problem 1442

Geometry Problem 1442.
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Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, Art, Poster, Typography, iPad Apps.

Problem 1441

Geometry Problem 1441.
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Intersecting Circles, Perpendicular Bisector, Parallel Lines, Art, Poster, Typography, iPad Apps.

Problem 1438

Geometry Problem 1438.
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Triangle, Incenter, Centroid, Circumcenter, Parallel, 90 Degree, Art, Poster, Typography, iPad Apps.

Problem 1437

Geometry Problem 1437.
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Intersecting Circles, Common Tangent, Equal Product, Art, Poster, Typography, iPad Apps.

Problem 1435

Geometry Problem 1435.
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Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points, Poster, Typography, iPad Apps.

Problem 1434

Geometry Problem 1434.
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Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement, Poster, Typography, iPad Apps.

Problem 1431

Geometry Problem 1431.
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Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Problem 1419

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

Problem 1417

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

Problem 1401

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

Problem 1396

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

Problem 1395

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

Problem 1394

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

Problem 1388 Circle, Triangle

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

Problem 1376 Isosceles Triangle, Circle

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

Geometry problem 1361

Geometry Problem 1361.
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Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Geometry problem 1351

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

Geometry problem 1345

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

Geometry problem 1335

Problem 1335. The Lune of Hippocrates has the same area of a Kite.
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Geometry problem 1325

Geometry Problem 1325.
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Octagons, Midpoints, Squares, Mobile Apps, iPad.

Geometry problem 1319

Geometry Problem 1319.
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Hexagons, Equilateral Triangles, Center, Midpoints.

Geometry problem 1317

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

Geometry problem 1316

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

Geometry problem 1315

Geometry Problem 1315.
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Triangle, Incircle, Tangent, Chord, Circle, Congruence.

Geometry Problem 902

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

Geometry problem 1301

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

Geometry problem 1282

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

Geometry problem 1253

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

Geometry problem 1238

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

Geometry problem 1233

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

Geometry problem 1212

Geometry Problem 1212
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Equilateral Triangle, Equilateral Hexagon, Concurrent Lines.

Geometry problem 1210

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

Geometry problem 1176

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

Six Tangential Quadrilaterals Theorem, problem 1175

Geometry Problem 1175: Six Tangential or Circumscribed Quadrilaterals Theorem
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Geometry problem 1168

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

Geometry problem 1143

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

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Last updated: May 24, 2020