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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Double eclipse
Tag: proportion
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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?
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Under the dome
Two semicircles with four squares and a yellow rectangle. What is the aspect ratio of the latter?
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Pull the string
Two regular hexagons and a circumcircle. What is blue : red?
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Fair scoop
What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?
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Antennas above and below
The triangle ABC has orthocentre H, so that HA is an antenna above the green hill. The rectangle BCDE is inscribed in the circumcircle (ABC). Show that HA = CD = BE.
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Crashing the kite
The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?
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No laughing matter
Two squares share a vertex. Each square contains a coloured rectangle with extended side. What’s green : blue? By Matthew Arcus.
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Sticky corners
Two equilateral triangles and several line segments. What is red : yellow?
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Vanishing point II
Six squares and four coloured triangles. What is red : blue : yellow : green?