ABC is an equilateral triangle. M is a point inside triangle ABC and, the respective feet of perpendiculars from M to the sides BC, CA and AB are denoted by D, E and F.
Determine the locus of all such points M for which / FDE is a right angle.
1. Construct congruent triangle A'BC as a reflection of ABC across line BC.
2. The part of the circle with origin A' and radius A'C that lies inside ABC represents the required locus.
3. The 3point circle intersecting B,M,C is equivalent.

Posted by broll
on 20101025 16:17:35 