A square containing a rectangle. What is the red fraction?
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Stars on 45
Category: Intermediate
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Staying in line
Three squares and a regular pentagon. Prove that the three red vertices are collinear.
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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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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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The square sail
A quadrilateral and a parallelogram share two sides, and a vertex from each determine the orange square. The lengths BC, EF, AD are 4,5,7 respectively, where E and F are midpoints of AB and DC. What is the orange area?
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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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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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Six six four
Two regular hexagons and a square. What’s the angle α?