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
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?

Categories
Intermediate

The cleaver

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

Categories
Intermediate

The twin triangles

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

Categories
Intermediate

Ice cube

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

Categories
Intermediate

The hourglass

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

Categories
Intermediate

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?

Categories
Intermediate

The ramp

A right triangle is split in two. What is the maximum yellow fraction?

Categories
Intermediate

Giro d’Italia

A square with the origin halfway one of its sides. The coordinates of two vertices are given. What is the square’s area?