What is the area of the coloured figure? Can you determine the area without counting the number of squares in each different-coloured shape?

## Baby steps

The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?

## The party hat II

An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?

## The lighthouse

A parallelogram and four equilateral triangles. What is yellow : green?

## Holes in my heart

The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?

## Tip of the veil

A square with two right angles. What fraction is yellow?

## The crosshairs

A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.

Some chords and segments inside a semicircle. What is the ratio of red to blue?

## Three times three

A regular nonagon and two equilateral triangles. What’s the angle α?

## The laser game

In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?