A semicircle containing two circles and two triangles. The blue right triangle connects three tangency points. Prove it is isosceles.

# Month: June 2021

## The triangle trio

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?

## The ragged mountain

A square containing three line segments of given length. What fraction is green?

## The two jabs

Two congruent equilateral triangles share a vertex. What is the angle α?

## 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 birdwatcher

Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

## 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?

## The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

## 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?