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## The boomerang

A quadrilateral and a triangle. What’s the angle α?

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## The pentagon proportion

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

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## Baby steps

The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?

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## The party hat II

An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?

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## Tip of the veil

A square with two right angles. What fraction is yellow?

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## The crosshairs

A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.

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## Three times three

A regular nonagon and two equilateral triangles. What’s the angle α?

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## The laser game

In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?

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