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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geometry puzzles for fun and beauty

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Four congruent squares plus another one. What is the angle α?

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A circle and a semicircle inside a square. What’s the length proportion of the two chords?

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Four squares, a rectangle and a circle. What is the proportion brown : grey?

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Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

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A rectangle and a square. What is the proportion purple : blue?

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A rectangle with two crossing line segments. What’s the minimal shaded fraction?

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A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

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A right triangle is split in two. What is the maximum yellow fraction?

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A square with the origin halfway one of its sides. The coordinates of two vertices are given. What is the square’s area?