Categories
Intermediate

The pentagon proportion

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

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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?

Categories
Advanced

The orange pennant

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

Categories
Intermediate

Getting stuck

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

Categories
Beginner

Family ties

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

Categories
Intermediate

The antenna

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