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## Touché

A square containing a rectangle and a tangent quarter circle. What fraction is orange?

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## Camera obscura

A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?

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## The pine forest

A square containing a quarter circle. What’s the proportion blue : brown : green?

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## The freight elevator

Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.

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## The red sash

Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?

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## The star gazer

A square divided by a diagonal and another line segment. What fraction of its area is purple?

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## The Eightfold Path

A semicircle, a square and an isosceles triangle. What’s the angle α?

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## Tomba La Bomba

Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?

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