Three squares and three common vertices. Prove that the quadrilateral ABCD is a rectangle.

Two equilateral triangles and a quarter circle that goes through both apexes. If the smaller triangle has area 1, what is the total shaded area?

## The rabbit hole

Three quarters of a unit square placed at the origin are shaded as shown. The remaining quarter is treated similarly but mirrored, and so on to infinity. What are the coordinates of the vanishing point?

## Up and down

A semicircle and a square. Three secants and a tangent form two triangles. What is their area proportion?

## The Chihuahua

A circle and a right triangle. What’s the angle α?

## The egg basket

A regular hexagon with a diagonal and a line segment connecting a vertex to a point on the other side. The two triangle areas are given. What is the hexagon’s area?

## The first cut

Using one straight cut, divide this triangle in two pieces. Paste them together to form a parallelogram with perimeter 19.

## Pandora’s box

A square containing five other squares. What fraction is coloured?

## Hold the line

Two squares and two equilateral triangles. Prove the three points are collinear.

## Another brick

A rectangle and a quarter circle. What is the area of the rectangle?