Problem of the Week 893

Morley's Ghost

ABCDEF is a hexagon inscribed in a unit circle with AB = CD = EF = 1. Let X, Y, Z, be the midpoints of the other three sides (i.e., of BC, DE, and FA). Prove that XYZ is an equilateral triangle.

(PS: If any of you find a non-trigonometry solution, do tell!)

© Copyright 1999 Stan Wagon. Reproduced with permission.

28 September 1999