prove that triangle $DEF$ is equilateral
Source: Canadian Mathematical Olympiad 2006, problem 5
January 28, 2007
geometry proposedgeometry
Problem Statement
The vertices of a right triangle inscribed in a circle divide the circumference into three arcs. The right angle is at , so that the opposite arc is a semicircle while arc and arc are supplementary. To each of three arcs, we draw a tangent such that its point of tangency is the mid point of that portion of the tangent intercepted by the extended lines . More precisely, the point on arc is the midpoint of the segment joining the points and where tangent at intersects the extended lines . Similarly for on arc and on arc . Prove that triangle is equilateral.