TR-MO 1995 Problem 4

In a triangle $ABC$ with $AB\neq AC$ , the internal and external bisectors of angle $A$ meet the line $BC$ at $D$ and $E$ respectively. If the feet of the perpendiculars from a point $F$ on the circle with diameter $DE$ to $BC,CA,AB$ are $K,L,M$ , respectively, show that $KL=KM$ .