A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?

# Month: July 2021

Five unit squares inside a larger square. What is the total area?

## The axe head

A tetrahedron with given vertex coordinates. What is its volume?

## The sleeping bag

A semicircle containing a circle. One line segment is tangent to the circle and connects to the semicircle centre. The chord connects two tangency points. What fraction is blue?

## A full house

Two large squares and three smaller ones of side length 5 are placed as shown. What is the pink area?

## The stained glass

Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?

## Tilted hourglass II

Two equilateral triangles inside a square. What’s the proportion green : orange?

## The hot-air balloon

Two circles, four tangent line segments and a square. What’s the proportion red : blue?

## The crazy diamond

Three rectangles and four triangles. Given that the red triangles have equal area, prove that the blue rectangles are similar.

## Partial eclipse II

Two diagonals of a circle are tangent to another circle. The chord passes through the tangency point. If the smaller circle has area 3, what is the area of the larger one?