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

# Tag: pentagon

## The crosshairs

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

## The vanilla ice cream

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

## Yeah, right!

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

## It’s all right II

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

## Fives and six

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

## The orange pennant

A regular pentagon with two coloured triangles. What’s the proportion orange : blue?

## Getting stuck

A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?

## Family ties

Two regular pentagons share a vertex. What is the proportion red : green?

## The antenna

A regular pentagon with an extended side. What’s the angle α?