Three circles (two with centre) and four line segments. Prove that, if the small circle is orthogonal to both wheels, then the wheels are also orthogonal to each other.
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The odd bicycle
Author: Rik D. Tangerman
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Above the line
A triangle cut by a line and four parallel line segments. Prove that green = red.
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Kazakov triangles
A circle with its centre and three triangles consisting of chords and radii. Express area X in terms of A, B and α.
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Unity
A square, a rectangle and two semicircles, one of which is centered in the shared vertex. What is yellow : blue?
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The Gakopoulos proportion
Two concentric quarter circles and a square. What is purple : red?
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Velocipede V
Two circles, a common tangent and several line segments. Prove that the red line segments are parallel.
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Sixtynine
A regular hexagon shares a side with a regular nonagon. What’s the angle α?
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Brick oven II
A rectangle inside a square. What fraction is yellow in terms of x?
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Spiegel im Spiegel II
A square containing a square with two extended sides. What is the blue fraction?
A quadrilateral with two diagonals and an inscribed circle. Prove that the three points are collinear.