A tetrahedron with given vertex coordinates. What is its volume?
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The axe head
Category: Intermediate
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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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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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The bishop’s hat
Two overlapping regular pentagons share two vertices. What fraction is the overlap area?
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The slippery slope
A semicircle, two squares and a triangle. What is the orange area?
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The rolling mill
A rectangle with a semicircle, a quarter circle and a common tangent. What fraction is blue?
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The holiday home
An isosceles triangle, a rectangle and two diagonals. What is the proportion green : blue?
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The glass pyramid
The vertices of an equilateral triangle are connected to an interior point. What is the angle α?