A circle with an inscribed regular pentagon, a square and a triangle. Prove that the point lies on the circumference of the circle.

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geometry puzzles to train your brain

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

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Two regular pentagons share a vertex. What’s the angle α?

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Two overlapping regular pentagons share two vertices. What fraction is the overlap area?

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A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

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A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?

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A square with two attached regular pentagons. A side and a diagonal are extended. What’s the angle?

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An equilateral triangle stacked on a pentagon. What’s the angle?

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Five equally sized peaches are closely packed in a pentagon-shaped box. Their midpoints are the vertices of a smaller pentagon. What fraction is shaded?