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

# Author: Rik D. Tangerman

## 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?

## The hex division

A regular hexagon with two diagonals and two perpendiculars. What’s red : yellow?

## The owl of Ceva

A triangle with three concurring cevians. What’s orange : blue?

## In the red

Two congruent semicircles with their centres and a chord. Prove that the two red triangles are congruent as well.

## The vanilla ice cream

A regular pentagon with two extended sides and a right angle. What is blue : green?

## Wheel of fortune

A unit square and a point on the inscribed circle. What is a^{2}+b^{2}+c^{2}+d^{2}?

Three congruent squares share two vertices while the upper sides coincide. What’s red : blue?

## Falling pillar II

Three congruent rectangles on a line. Prove that the four red points are cyclic.

## The falling pillar

Three congruent rectangles on a line. What’s the angle α?