A regular hexagon, a square and a rectangle. What is the area proportion rectangle : square?

## A clear vision

A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?

## Star and stripes

Two concentric congruent squares and two red rectangles. What fraction of the total area is red?

## The inner parallel

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

## 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?