Categories

## The Magdeburg hemispheres

A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?

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## Band-Aid

Five unit squares inside a larger square. What is the total area?

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A tetrahedron with given vertex coordinates. What is its volume?

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## The sleeping bag

A semicircle containing a circle. One line segment is tangent to the circle and connects to the semicircle centre. The chord connects two tangency points. What fraction is blue?

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## A full house

Two large squares and three smaller ones of side length 5 are placed as shown. What is the pink area?

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## The stained glass

Two congruent rectangles are placed side by side. Two line segments form two coloured quadrilaterals and three triangles. What is the proportion purple : green?

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## Tilted hourglass II

Two equilateral triangles inside a square. What’s the proportion green : orange?

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## The hot-air balloon

Two circles, four tangent line segments and a square. What’s the proportion red : blue?

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## The crazy diamond

Three rectangles and four triangles. Given that the red triangles have equal area, prove that the blue rectangles are similar.

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## Partial eclipse II

Two diagonals of a circle are tangent to another circle. The chord passes through the tangency point. If the smaller circle has area 3, what is the area of the larger one?