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## Tilted hourglass III

A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?

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## Primary colours

An equilateral triangle inside a rectangle. What is red : yellow : blue?

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## The same vein

Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.

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## Equal rights

Two squares sharing a vertex. Two vertices are connected by a line segment. What is yellow : green?

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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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## In touch

A regular nonagon and four equilateral triangles. The purple and yellow triangles share a vertex. Prove that the yellow triangles also share a vertex.

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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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## The lighthouse

A parallelogram and four equilateral triangles. What is yellow : green?

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## Tip of the veil

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