geometry puzzles

Category: Intermediate

The reflection principle

A green triangle with several line segments. Prove that the red point is its orthocentre.

Three squares and two perpendicular line segments. What is red : yellow : blue?

A rectangle containing a right triangle. What’s red : blue?

Two regular pentagons and a circle through four vertices and two intersection points. What is is the green overlap fraction?

Two squares sharing a vertex, a diagonal and a line segment. Prove that the two angles are congruent.

Two squares and an equilateral triangle. The three red line segments meet in a point. What is the yellow fraction?

Two semicircles with parallel bases. Show that HF and GE intersect on the perpendicular line to AC above A.

An equilateral triangle inside a rectangle. What’s red : yellow : blue?

A triangle with two circles and two line segments. Prove that it is isosceles.

A square with a circle and a tangent. The tangency point lies on the diagonal. What fraction is red?