106 geometry problems

106 Geometry Problems -

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

Redraw cleanly. Mark given equalities, angles, midpoints, tangents. 106 geometry problems

What would prove it? Congruence? Concyclicity? Equal angles? Equal products (Power of a point)? Collinearity (Menelaus)? Common tricks: reflect a point across an angle

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

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.).

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

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

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

What would prove it? Congruence? Concyclicity? Equal angles? Equal products (Power of a point)? Collinearity (Menelaus)?

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

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.).

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