Four squares and two shared vertices. What fraction is blue?

## An irregular tiling

A triangle divided by three line segments. What fraction is blue?

## The guylines

Two squares and an extended side. What’s the angle α?

## Cross the line

An equilateral triangle with two line segments crossing exactly on the semicircle. What is the proportion red : green?

## The baby block

Two squares and an extended side. Prove that red : green = blue : yellow.

## The England win

A unit square containing two red overlapping congruent rectangles. If they cover exactly half the square’s area, what is their width x?

## A fair division

A square with a diagonal and a right triangle. What’s the proportion blue : red?

## The steam locomotive

Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?

## The inner circle

A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?

## Know all angles

A triangle with its circumcircle and circumcentre. What’s α : β?