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 3-point circle intersecting B,M,C is equivalent.

Posted by broll on 2010-10-25 16:17:35