Question 85
A circle touches the side $BC$ of a triangle $ABC$ at the vertex $B$ and intersects the side $AC$ at the vertex $A$ and a point $E$. Another circle touches the side $BC$ at the vertex $C$ and intersects the side $AB$ at the vertex $A$ and a point $D$. $F$ is the point of intersection of the line segments $BE$ and $CD$. Prove that the triangle $BCF$ is isosceles.
