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## Four five

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

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## Orthogonal partial eclipse

Two circles are orthogonal (tangents at intersections are perpendicular). How must the points A and B be related?

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## Folding to pyramid

A square and an equilateral triangle. The square is folded as shown. What is 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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## The boot

Two squares and some line segments. Find the relation between the angles α and β.

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## What’s your angle?

Six squares are placed as shown. What’s the angle α?

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## Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

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## Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

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## Six six four

Two regular hexagons and a square. What’s the angle α?

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## Square offspring

Three squares and two line segments. What’s the angle α?