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## True colours

In this right triangle, if red = blue, what is orange : purple?

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## We are equal

A quadrilateral with its diagonals. What’s the angle α?

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## A nice percentage

An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α?

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## The gremlin

Two circles and three coloured isosceles triangles. Prove that the circles are concentric.

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## The Pappus eggs

Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.

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## The chain

Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?

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## Sliding down

Two squares share a vertex. One line segment connects their centres, another two vertices. What is the length proportion blue : red?

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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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