geometry puzzles

Category: Intermediate

To shy away

Two squares share a vertex. What’s the proportion orange : blue?

Two overlapping congruent rectangles. What’s the angle α?

A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?

Two concentric congruent squares and two red rectangles. What fraction of the total area is red?

Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?

Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?

An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?

Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?

Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.

A square contains an isosceles triangle with an extended altitude. What fraction is mahogany?