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Tip of tipi

A regular hexagon is divided in four triangles and one quadrilateral. Express the hexagon area in terms of areas A, B and C.

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The Dutch roll

Two regular hexagons share a vertex. What is the angle α?

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Hex division II

A regular hexagon and two equals angles. What is blue : green : red?

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Stand behind

Two regular hexagons share a vertex. Prove that the blue points are collinear.

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Pull the string

Two regular hexagons and a circumcircle. What is blue : red?

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Six six four

Two regular hexagons and a square. What’s the angle α?

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The punctured hexagon

A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.

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Four six four

A regular hexagon and two similar rectangles. What fraction is green?

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Six four

A regular hexagon and an inscribed tilted rectangle. What is the angle α?

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Ball of yarn

A cyclic hexagon has concurrent cross diagonals. What is the ratio of the product of the orange sides compared to the product of the purple sides. (ace:bdf).