Categories
Beginner

The pit

A regular hexagon, a square with its diagonals, an equilateral triangle and a circle. Prove that the hexagon and the circle are concentric.

Categories
Intermediate

The dance

A regular hexagon, two squares and a semicircle connecting two vertices. Is the red vertex located on the semicircle?

Categories
Intermediate

Tomba La Bomba

Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?

Categories
Advanced

Mind the gap

A regular hexagon with an equilateral triangle sharing a vertex and having a vertex somewhere along the opposite side. What is the maximum length of line segment g?

Categories
Intermediate

The bubble chamber

A regular hexagon and two semicircles connecting vertices. What’s the angle α between the chords?

Categories
Beginner

The life net

The vertices of a regular hexagon are connected to midpoints of opposing sides. What fraction is red?

Categories
Beginner

The Sikh turban

A regular hexagon containing an orange quadrilateral. What fraction of the total area is blue?

Categories
Intermediate

The honeycomb

Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?

Categories
Beginner

The blue pill

A regular octagon containing a blue hexagon. All line segments have equal length. What fraction is blue?

Categories
Intermediate

The Lion King II

A regular hexagon and three squares. What is the proportion yellow : brown?