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.)
A quarter circle with a right triangle. Prove that the red point is the incentre of this triangle.
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 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?
What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?
A circle containing two internally tangent circles. Prove that the red triangle is isosceles.
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.
The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?