Two triangles share a side. What’s the angle β?

## The wall between us

Two circles inscribed an a trapezium divided by a perpendicular line segment. What is the proportion of its length a and the side b?

## Arc de Triomphe

A parabola passing through a square’s bottom vertices and tangent to its top side. What fraction is blue?

## The minor chord

Three chords meet at the same point on the circumference of the circle. A perpendicular line segment divides one of them in two parts of length a and b. Express the length of the smallest chord x in terms of a and b.

## The giant’s shoulder

Two equilateral triangles inside a square. What’s the proportion orange : blue?

## Buddha’s belly

A square containing a quarter circle and a tangent line segment. What is a : b?

## The bubble chamber

A regular hexagon and two semicircles connecting vertices. What’s the angle α between the chords?

## The stuck boulder

A rectangle contains a circle wedged between two triangles. What is the circle radius in terms of triangle heights a and b?

## The ball pool

A square having side length 12 contains a quarter, semi and full circle. The centres of the latter two are connected to the square’s centre to form a green triangle. What is it’s area?

## Square eyes

A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?