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Lines, angles, figures,
Puzzles waiting to be solved,
Geometry fun.
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Open Geometry Problems
Problems
Ten Geometry Problems
Visual Index
Parallel lines
Perpendicular lines
Collinear Points
Triangle
Metric Relations
Quadrilateral
Triangle & Squares
Polygons
Pentagons
Hexagons
Heptagons
Octagons
Circle
Triangle
Centers Congruence
Similarity, Ratios, Proportions |
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Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. |
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Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits. |
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Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!. |
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Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
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Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
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Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
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Geometry
Problem 1535: Crack the Code: Inscribed Circle in Square - Angle Challenge! Solve the Mystery. |
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Geometry
Problem 1534: High School Brainteaser: Tangent Circles, Common External Tangent, and Angle Conundrums!.
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Geometry
Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square - A High School Challenge.
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Geometry
Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle! - A High School Challenge.
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Geometry
Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord - A High School Challenge.
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Geometry
Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure Today! - A High School Challenge.
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Geometry
Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge.
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Geometry
Problem 1528: Cracking the Circle Code: Unveiling the Tangent and Angle of an Inscribed Circle within a 90-Degree Circular Sector.
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Geometry
Problem 1527: Discovering the Hidden Angle: Solving the Puzzle of Two Intersecting Circles.
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Geometry
Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.
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Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. |
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Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. |
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Geometry
Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle - Get Expert Geometry Tips Now!
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Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. |
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Geometry
Problem 1521 and a Thematic Poem.
Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. |
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Geometry
Problem 1520 and a Thematic Poem.
Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge. |
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Geometry
Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines. |
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Geometry
Problem 1518 and a Thematic Poem.
Boost Your Geometry Skills: Solve for the Number of Sides in an Equiangular Polygon with an Interior Point and Bisected Angle. |
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Geometry
Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School. |
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Geometry
Problem 1516 and a Thematic Poem.
Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School. |
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Geometry
Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School. |
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Geometry
Problem 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two
Sides. Difficulty Level: High School. |
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Geometry
Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School. |
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Geometry
Problem 1511 and a Thematic Poem.
Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School. |
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Geometry
Problem 1510 and a Thematic Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School. |
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Geometry
Problem 1509 and a Thematic Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School. |
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Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. |
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Geometry
Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School. |
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Geometry
Problem 1506.
Parallel Rays, Angles, Corresponding, Alternate. |
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Geometry
Problem 1505.
Parallel Rays, Angles, and Bisector, Corresponding, Alternate, Conjugate. |
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Geometry
Problem 1504 and Poem.
Squares, Equilateral Triangle, Parallel, Angle. |
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Geometry
Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular. |
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Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. |
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Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. |
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Geometry
Problem 1500.
Circle, Perpendicular, Tangent, Secant, Cyclic Quadrilateral, Parallel, Similarity, Measurement. |
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Geometry
Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction. |
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Geometry
Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points. |
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Geometry
Problem 1497.
Triangle, Transversal, Same Ratio, Proportionality, Isosceles, Double Angle. |
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Geometry
Problem 1496.
Triangle, Congruence, Isosceles, Double Angle, 30 Degrees. |
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Geometry
Problem 1495.
Circle, Parallel Chords, 30 Degree Angle, Radius Squared. |
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Geometry
Problem 1494.
Parallelogram, Midpoints, Octagon, Areas. |
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Geometry
Problem 1493.
Four Squares, Parallelogram, Auxiliary Lines. |
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Geometry
Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement. |
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Geometry
Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement. |
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Geometry
Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement. |
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Geometry
Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement. |
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Geometry
Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement. |
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Geometry
Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement. |
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Geometry
Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement. |
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Geometry
Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement. |
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Geometry
Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement. |
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Geometry
Problem 1483.
Isosceles Right Triangle, Excenter, Perpendicular, Measurement. |
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Geometry
Problem 1482.
Right Triangle, Perpendicular, Double Angle, Measurement. |
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Dynamic Geometry 1481.
Five Tangential or Circumscribed Quadrilaterals, Pitot Theorem, Congruence, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1480.
Japanese Theorem for Cyclic Polygon, Sangaku, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector,
Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1478.
Cyclocevian, Reuschle-Terquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra,
iPad. |
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Dynamic Geometry 1475.
Clifford Intersecting Circles Theorem, Step-by-step Illustration, GeoGebra, iPad. |
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Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Step-by-step Illustration. |
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Dynamic Geometry 1472.
Cyclic Quadrilateral, Perpendicular Diagonals, Rectangle, Step-by-step Illustration. |
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Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Step-by-step Illustration. |
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Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent,
Parallel, Rhombus, Step-by-step Illustration. |
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Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration. |
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Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration. |
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Geometry Problem 1467.
Square, Rectangle, Triangle, Area. |
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Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
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Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
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Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines. |
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Dynamic Geometry
1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Step-by-step Illustration using GeoGebra. |
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Geometry
Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra. |
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Geometry
Problem 1458.
Triangle, Incircles, Excircle, Area, Step-by-step Illustration using GeoGebra. |
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Geometry
Problem 1457.
Altitudes, Circles, Similarity,
Product of the Inradii Lengths,
iPad. Step-by-step illustration using GeoGebra. |
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Geometry
Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area,
iPad. Step-by-step illustration using GeoGebra. |
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Geometry
Problem 1455.
Nagel Point, Excircles, Incircle, Congruent Segments,
iPad. Step-by-step illustration using GeoGebra. |
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Geometry
Problem 1454.
Intersecting Circles, Perpendicular Lines, Cyclic Quadrilateral, Collinear
Points,
iPad. Step-by-step illustration using GeoGebra. |
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Geometry
Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points,
iPad. |
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Dynamic Geometry 1452.
Japanese Theorem, Sangaku,
Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step
illustration using GeoGebra. |
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Dynamic Geometry 1451.
Orthopole of a Line. Step-by-step
illustration using GeoGebra. |
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Dynamic Geometry 1450.
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step
illustration using GeoGebra. |
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Geometry Problem 1400. Triangle with three rectangles on the sides, Perpendicular Bisectors, Concurrency. |
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Geometry Problem 1391. Two Triangles, Ratio of Areas, Circumcircle. |
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Geometry Problem 1381. Parallelogram, Exterior Point, Triangle, Area. |
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Geometry Problem 1371: Equilic
Quadrilateral 5 |
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Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. |
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Geometry Problem 1200
Square, Right Triangle, Perpendicular, 90 Degrees, Equal Areas. |
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Geometry Problem
900
Intersecting Circles, Common External Tangent, Secant, Angle, Congruence.
GeoGebra, HTML5 Animation for Tablets.
Solution. |
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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.
Solution. |
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Geometry Problem
700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.
Solution. |
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Geometry Problem
600
Circle, Area, Tangent, Semicircle, Tangency Point.
Solution. |
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Geometry Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure.
Solution. |
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Geometry Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.
Solution. |
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Geometry Problem 300.
Tangents to a circle, Secants, Square.
Solution. |
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Geometry Problem 200.
Right Triangle, Incircle, Excircles, Points of
Tangency, Inradius.
Solution. |
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Geometry Problem 100.
Circle
Area, Archimedes' Book of Lemmas.
Solution. |
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Geometry Problem
1.
Triangle, median, angles, 45 degrees.
Solution |
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