Category: 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?

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

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

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

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

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

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

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

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

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