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Pentagon pleasure II

A regular pentagon and its circumcircle. What is blue : orange?

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Pentagon offspring II

Two regular pentagons, one of which has an extended side. What’s the angle α?

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The happy couple

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

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Tipping point II

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

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Ice cream cone II

Two regular pentagons sharing a vertex with extended sides and diagonals. Proof that the three red points are collinear.

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Four five

A square and a regular pentagon share a vertex. What’s the angle α?

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Outside the pentagon II

A regular pentagon and two equilateral triangles. What’s the angle α?

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Staying in line

Three squares and a regular pentagon. Prove that the three red vertices are collinear.

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Pentagon pleasure

Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?

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Pentagon divided

Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. But you may divide a segment into a number of equal segments for free.)