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## 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.

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## The dance

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

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## Tomba La Bomba

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

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## 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?

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## The bubble chamber

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

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## The life net

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

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## The Sikh turban

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

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## 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?

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