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## The balancing act

A square with two perpendicular lines. What is the minimal blue fraction?

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## The commons

Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?

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## Softening the edges

A quarter circle contains a semicircle and a square. What fraction of the area is purple?

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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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## The folded napkin

A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?

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## Together we stand

Two squares sharing a vertex. What’s the angle α?

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## The pleasure dome

A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?

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