A rectangle with three touching quarter circles. What fraction of its area is coloured?

## The balancing act

A square with two perpendicular lines. What is the minimal blue fraction?

## The commons

Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?

## Softening the edges

A quarter circle contains a semicircle and a square. What fraction of the area is purple?

## The Sikh turban

A regular hexagon containing an orange quadrilateral. What fraction of the total area is blue?

## The honeycomb

Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

## The folded napkin

A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?

## Together we stand

Two squares sharing a vertex. What’s the angle α?

## The pleasure dome

A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?

## Twin peaks

A rectangle with three line segments. What is the proportion yellow : red?