Categories
Intermediate

Sisyphus

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

Categories
Intermediate

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?

Categories
Beginner

The ragged mountain

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

Categories
Beginner

The two jabs

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

Categories
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?

Categories
Advanced

The birdwatcher

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

Categories
Intermediate

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?

Categories
Beginner

The hammock

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

Categories
Intermediate

Lazy Friday

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

Categories
Intermediate

The fez

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