A triangle cut by a line and four parallel line segments. Prove that green = red.
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Above the line
Tag: length
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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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Egg of Columbus
An ellipse with its focal points, major and minor axis. What is x, the distance from the centre to the right focal point?
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The Roman katapult
Two quarter circles and a circle with a tangent line segment. What is pink : green?
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Ice cream cone III
A triangle with its incircle and a cevian. What is red : yellow?
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Slip sliding
Two squares share a vertex. The shown vertex can lie anywhere on the lower side. What is the maximum of red/blue?
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Compartments
An equilateral triangle with a cevian and two inscribed circles. What is yellow : red?
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Crossing lengths
A cyclic quadrilateral (CDIF), where we form two segments: MK (green) with DM perp to FC and DK perp to FI; GJ (orange), with IG perp to FC and IJ perp to CD. What is the ratio MK:GJ ? What about MN:GN?
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Lunar ratios
A circle of radius r is interior-tangent to the larger yellow circle of radius R, with diameters overlapping. Express s/k in terms of r and R.