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

A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?
A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.
A regular pentagon with two extended sides and a right angle. What is blue : green?
A regular pentagon with three line segments. What’s the angle α?
A regular pentagon and a right triangle. What’s the angle α?
Two regular pentagons and a circle through four vertices and two intersection points. What is is the green overlap fraction?
A regular pentagon with two coloured triangles. What’s the proportion orange : blue?
A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?
Two regular pentagons share a vertex. What is the proportion red : green?
A regular pentagon with an extended side. What’s the angle α?