Categories
Beginner

The boomerang

A quadrilateral and a triangle. What’s the angle α?

Categories
Intermediate

The pentagon proportion

A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?

Categories
Advanced

Baby steps

The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?

Categories
Intermediate

The party hat II

An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?

Categories
Beginner

Tip of the veil

A square with two right angles. What fraction is yellow?

Categories
Advanced

The crosshairs

A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.

Categories
Intermediate

Three times three

A regular nonagon and two equilateral triangles. What’s the angle α?

Categories
Advanced

The laser game

In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?

Categories
Advanced

The vanilla ice cream

A regular pentagon with two extended sides and a right angle. What is blue : green?

Categories
Beginner

The falling pillar

Three congruent rectangles on a line. What’s the angle α?