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(Last Update: 24 February 2022)
"A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery". - George Polya in How to Solve It (Princeton 1945).
"In real mathematics, the answers are not in the back of the book nor are the problems simply variations of preceding, carefully worked examples. In fact, in real mathematics, there is no book at all - no ready-made questions and problems; even those one has to invent oneself!"
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Area Ratios of Inscribed Polygons Medium-Hard
Bicentric Quadrilateral Construction Challenge Medium - Hard
Bottema's Theorem aka Carnot's Theorem Easy-Medium (Updated!)*
British Mathematics Olympiad Concurrency Problems Medium
Bug Escape Problem Easy
Circle Circumference Result Easy-Medium
Clough's Conjecture Medium-Hard
Collinear Conjecture Easy-Medium
Concurrent Angle Bisectors of Quadrilateral Easy (NEW!*)
Conic by Half-turn Medium
Cyclic Quadrilateral Difference of Squares Theorem Hard (NEW*!)
Cyclic Quadrilateral Rectangle Result Medium
Desargues' Theorem Easy-Medium
Descartes' Geometric Solving of Some Quadratics Easy-Medium
Diagonal Division Ratios in a Quadrilateral Hard (NEW!)
Dirk Laurie Tribute Problem Medium (NEW!*)
Double Angle Triangle Medium
Dynamic Art: A Parquet Deformation Tiling An art project idea (Updated!*)
Equi-inclined Lines Problem Easy (NEW!*)
The Equi-partitioning Point of a Quadrilateral Easy (NEW!*)
Euclid 1-43 Parallelogram Area Theorem Easy-Medium
Extangential Quadrilateral Medium (NEW!*)
Finding the Median and Centroid of a Triangle by Experimentation: A gravity simulation Use to explore. (Updated!)*
Finding the centroid of a triangle with different weights at the vertices: A gravity simulation Use to explore. (Updated!)*
Generalizing Viviani's theorem to 3D Easy to Medium.
Geometry Loci Doodling with a Cyclic Quadrilateral. Medium - Hard. (NEW!*)
Gielis Super Shape Formula Medium. (Updated!)
Golden Quadrilaterals (generalizing a 'golden rectangle' Medium. (NEW!*)
Hexagon Explorations Easy
Hippocrates' Theorem Easy (Updated!*)
IMO 2014 Problem 4 (Geometry) Medium-Hard (Updated!*)
Interior Angle Sum of Polygons: a General Formula Easy-Medium (Updated!*)
Interesting Collinearity Medium-Hard (NEW!)
Intersecting Circles Easy (NEW!)
Jannie's Father's Farm Problem Easy - Medium
Kinky Lines Easy
Klingen's Theorem of two intersecting circles or two adjacent isosceles triangles Medium - Hard (Updated!*)
The Lux problem Medium - Hard (NEW!*)
Matric Geometry Exam Question - 1949 Easy - Medium
Napoleon Variation Problem Medium
Over and over: two geometric iterations with triangles Medium - Hard
Parallelogram Distances Easy (NEW!*)
Parallelogram Trio Medium
Paul Yiu's problem and a generalization Medium (Updated!*)
Pi in other geometries Medium
Pompe's Hexagon Theorem Medium-Hard (NEW!*)
Pythagorean Quadrilateral 1 Medium
The quasi-circumcentre and quasi-incentre of a quadrilateral Medium (Updated!*)
SA Mathematics Olympiad Problem 2022, Round 2, Question 25 Medium - Hard (NEW!*)
Side trisection triangle concurrency Easy - Medium
Similar Triangles Easy
Square Trigonometry Easy
Tangential Quadrilateral Converse. Medium (NEW!*)
Tangential Quadrilateral - Pitot's Theorem. Easy (NEW!*)
Tangential Quadrilateral - Theorem of Gusic & Mladinic. Easy - Medium (NEW!*)
Tangential Hexagon Incircles Application. Medium (NEW!*)
Theorem of Arsalan Wares Easy-Medium (Updated!*)
Trapezoid Explorations Medium
Trapezoid Explorations Medium
Triangle Incentre-Circumcentre Collinearity Easy-Medium
Two circles result Easy
Two different centroids (balancing points) of a quadrilateral Easy-Hard (Updated!)*
Last modified by Michael de Villiers, 24 February 2022.
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