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## The wall socket

Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.

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## The remote corner

A square and a circle. What is the green area?

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## The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?

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## Fair and square

Two squares of which three vertices form an isosceles triangle. What is the angle α?

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## The double helix

Five equidistant parallel line segments. What’s the proportion green : red?

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## The push-up

Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?

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## The glass ceiling

Three squares, two of which share a vertex. What is the total area?

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## The golf ball

A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.

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