Three triangles, one of which is right and one is isosceles, form a large triangle. Two side lengths are given. What fraction of the total area is red?

# Category: Intermediate

## The single parent holiday

An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?

## The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

## Lazy Friday

Four congruent squares plus another one. What is the angle α?

## The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

## The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?

## The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

## Ice cube

A rectangle and a square. What is the proportion purple : blue?

## The hourglass

A rectangle with two crossing line segments. What’s the minimal shaded fraction?

## Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?