A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?

# Author: Rik D. Tangerman

## Primary colours

An equilateral triangle inside a rectangle. What is red : yellow : blue?

## The same vein

Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.

## Equal rights

Two squares sharing a vertex. Two vertices are connected by a line segment. What is yellow : green?

## The boomerang

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

## The pentagon proportion

A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?

## In touch

A regular nonagon and four equilateral triangles. The purple and yellow triangles share a vertex. Prove that the yellow triangles also share a vertex.

## 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?

## Tip of the veil

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