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## Colour confinement

A semicircle with three tangent line segments. What is its area in terms of lengths a and b?

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## Two steps forward

Two equilateral triangles share a vertex and have their bases on the same line. A third equilateral triangle is constructed from their apexes. Prove that its apex is also on that line.

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## The earth projection

A circle touching a semicircle and a triangle. What is the proportion blue : green?

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## Crazy frog

A regular pentagon, two semicircles and two chords. What’s the length proportion a : b?

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## Composition in red, blue and yellow

A rectangle containing red and blue squares and a yellow rectangle. What is the proportion red : (blue+yellow)?

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## The dark lord

Two congruent equilateral triangles and two squares. What’s the angle α?

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## The pointy shoe

A quarter circle, a semicircle and a triangle. What’s the angle α?

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## Cordon sanitaire

Two perpendicular lines and a third line. Four circles are tangent to all three lines. Prove that their areas satisfy AB=CD.

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