A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?

# Author: Rik

## The pine forest

A square containing a quarter circle. What’s the proportion blue : brown : green?

## The freight elevator

Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.

## The red sash

Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?

## The star gazer

A square divided by a diagonal and another line segment. What fraction of its area is purple?

## The Eightfold Path

A semicircle, a square and an isosceles triangle. What’s the angle α?

## Tomba La Bomba

Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?

## The augmented chord

A circle with four chords. What is the length of line segment x in terms of lengths a and b?

A semicircle, a square and a chord. If the square has area 32, what is the semicircle area?

## The dome tent

A rectangle with a diagonal and an inscribed semicircle. What is red : green : blue?