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Cradle of waves
What is the area of the entire figure (in terms of x) given that the segments AB, CD, EF,…, QR are all semicircle diameters, and the lengths decrease geometrically ( AB=2, CD = 2x, EF= 2x^2, GH = 2x^3,…)?
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Stars on 45
A square containing a rectangle. What is the red fraction?
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Video: Pandora’s box II
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Staying in line
Three squares and a regular pentagon. Prove that the three red vertices are collinear.
Two squares and some line segments. Find the relation between the angles α and β.
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Video: What’s your angle?
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Four squares
How does the average of the areas of the blue and green squares compare with the area of the purple square?
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Video: Pentagon pleasure
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Double eclipse
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.)