geometry puzzles

Category: Intermediate

Above the line

A triangle cut by a line and four parallel line segments. Prove that green = red.

A square, a rectangle and two semicircles, one of which is centered in the shared vertex. What is yellow : blue?

Two concentric quarter circles and a square. What is purple : red?

A regular hexagon shares a side with a regular nonagon. What’s the angle α?

A square containing a square with two extended sides. What is the blue fraction?

An ellipse with its focal points, major and minor axis. What is x, the distance from the centre to the right focal point?

Two quarter circles and a circle with a tangent line segment. What is pink : green?

Four triangles in a rectangle. The three red triangles have equal areas. What is blue : red?

Two squares share a vertex. The shown vertex can lie anywhere on the lower side. What is the maximum of red/blue?

Three congruent squares and an equilateral triangle. What is blue : orange?