Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

## The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

## The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

## Lazy Friday

Four congruent squares plus another one. What is the angle α?

## The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

## The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

## The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?

## The green field

A square is divided in two quadrilaterals of given area. What fraction of the square’s perimeter is red?

## The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

## The partial eclipse

Two circles and a radius connecting their centres. What is the length of the parallel chord?