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,…)?
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.)
Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.
Two regular pentagons. The centre of the large one is a vertex of the small one. What is yellow : green?
Two semicircles with four squares and a yellow rectangle. What is the aspect ratio of the latter?
Two regular hexagons and a circumcircle. What is blue : red?
The triangle ABC has orthocentre H, so that HA is an antenna above the green hill. The rectangle BCDE is inscribed in the circumcircle (ABC). Show that HA = CD = BE.
A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.
Two equilateral triangles and several line segments. What is red : yellow?
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)