A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.

# Author: Rik

## Letting go

Two squares share a vertex. Three other vertices are collinear. What is the area proportion of the blue to the red square?

## Orange above

A square contains a right triangle. What fraction is orange?

## The double flag

Three tangent circles and a common tangent. The three tangency points are shown. What is α + β?

## The door stop

A triangle with a cevian. What is α?

## Four to twelve

A regular dodecagon and a square share two vertices. What is the area proportion square : dodecagon?

## The japanese progression

An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?

## The triangular tiling

A rectangle is divided into four similar triangles. What fraction is blue?

## The righteous four

Four rectangles. The green and red rectangle are similar. What’s the area proportion of the orange and the blue rectangle?

## The gyroscope

Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.