106 Geometry Problems [2026]

Do you see: cyclic quad? right triangle? homothety between incircle/excircle? radical axis? spiral similarity?

This is a tall order, but a great one. 106 Geometry Problems (often referring to the book by Titu Andreescu, Vlad Crisan, and Bogdan Enescu, or the classic "103 Trigonometry Problems" / "106 Geometry Problems" from the AwesomeMath series) is an for high school students targeting Olympiads (IMO, USAMO, etc.). 106 geometry problems

What would prove it? Congruence? Concyclicity? Equal angles? Equal products (Power of a point)? Collinearity (Menelaus)? Do you see: cyclic quad

Common tricks: reflect a point across an angle bisector, draw the second intersection of two circles, construct the circumcircle of three points. radical axis

If stuck for 20 min, switch to coordinates/complex numbers (but only if allowed in contest – IMO accepts pure synthetic or analytic).

Redraw cleanly. Mark given equalities, angles, midpoints, tangents.