Categories
Beginner

Projection bias

Two regular pentagons are placed side by side. What’s the proportion blue : green?

Categories
Beginner

The pentagon attack

Two regular pentagons and two diagonals. What’s the angle α?

Categories
Beginner

The three day stubble

A regular pentagon and a square share two vertices. What’s the angle α?

Categories
Intermediate

Mickey Mouse

Three regular pentagons and two extended sides. What fraction of the total area is red?

Categories
Beginner

The outsider

A circle with an inscribed regular pentagon, a square and a triangle. Prove that the point lies on the circumference of the circle.

Categories
Intermediate

Crazy frog

A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?

Categories
Beginner

The pentagon push

Two regular pentagons share a vertex. What’s the angle α?

Categories
Intermediate

The bishop’s hat

Two overlapping regular pentagons share two vertices. What fraction is the overlap area?

Categories
Advanced

Tympanum II

A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

Categories
Advanced

The tympanum

A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?