Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)

# Tag: square

## Pop you bubble

A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.

## The ceiling lamp

A regular octagon with two diagonals and a square. Prove that the four red points are concyclic.

## Stay centred

Two squares share a vertex. Prove that the red point is the circumcentre of the red triangle.

## Peeping out II

A unit square and a rectangle touching three square sides and passing through the midpoint of the upper side. What is the minimal blue area?

## Peeping out

A unit square and a rectangle. What is the blue area?

## Pythagoras times three

Three squares on a grid. What is the ratio of the areas red : green : purple?

## Bottoming out II

A semicircle with three squares. What’s the angle α?

## The heptagon square

What is the angle α between the blue line and the baseline of the orange square?

## A golden year

Two squares, a rectangle and a semicircle. What is yellow : green?