Categories
Intermediate

Playing fields

Show equality of the green and orange square playing field areas.

Categories
Beginner

Folding a pentagon

One side of a regular pentagon is folded back and forth as shown. Are the six red line segments congruent?

Categories
Intermediate

The telescope

The odd regular polygons are stacked together, in increasing order, zigzagging to form a telescope that extends forever! What is the limiting angle (with respect to the horizontal) at which the telescope points?

Categories
Beginner

Outside the pentagon

A regular pentagon and two coloured equilateral triangles. What is 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

The crosshairs

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

Categories
Advanced

The vanilla ice cream

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

Categories
Intermediate

Yeah, right!

A regular pentagon with three line segments. What’s the angle α?

Categories
Advanced

It’s all right II

A regular pentagon and a right triangle. What’s the angle α?

Categories
Intermediate

Fives and six

Two regular pentagons and a circle through four vertices and two intersection points. What is is the green overlap fraction?