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,…)?
A square containing a rectangle. What is the red fraction?
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.
How does the average of the areas of the blue and green squares compare with the area of the purple square?
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.)
A quarter circle with a right triangle. Prove that the red point is the incentre of this triangle.