A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?
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The Magdeburg hemispheres
Month: July 2021
Five unit squares inside a larger square. What is the total area?
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The axe head
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?