Categories
Intermediate

Locus pocus

The blue vertex is fixed in the plane. The green vertex can be anywhere on a circle. The yellow vertex completes an equilateral triangle. What is the locus of the yellow vertex?

Categories
Advanced

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.)

Categories
Intermediate

Hidden circle II

What is the locus of orange points for which the purple lines are parallel? The fixed cevians of the triangle BCD are angle bisectors.