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## Sisyphus

A semicircle containing two circles and two triangles. The blue right triangle connects three tangency points. Prove it is isosceles.

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## The triangle trio

Three triangles, one of which is right and one is isosceles, form a large triangle. Two side lengths are given. What fraction of the total area is red?

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## The ragged mountain

A square containing three line segments of given length. What fraction is green?

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## The two jabs

Two congruent equilateral triangles share a vertex. What is the angle α?

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## The single parent holiday

An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?

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## The birdwatcher

Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

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## The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

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## The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

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