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Double eclipse
Given green and blue discs, construct a red region so that for every ray leaving L stays in the blue region exactly as long as it does in the pink region. (Namely, KM = OL.)
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The belly button
A quarter circle with a right triangle. Prove that the red point is the incentre of this triangle.
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Video: Under the dome
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Pandora’s box II
Five squares and a diagonal. What fraction of the largest square is coloured?
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What’s your angle?
Six squares are placed as shown. What’s the angle α?
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Video: Pull the string
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Steam roller
Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.
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Video: Mother’s umbrella
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Pentagon pleasure
Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?