Three discs have one 3-way common point on their boundaries. Where do the red rays intersect? How are the points of intersection related to the common boundary point?
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When worlds collide
Month: June 2025
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The odd bicycle
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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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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Flower of gears
During one step every internal polygon rotates to the next position along its outer polygon, merging two green sides. How many full turns are made by the innermost triangle before the entire configuration returns to its initial state?
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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?