Question 56
Through a point $F$ outside a circle $k$, a tangent $FA$ and a secant $\ell$ are drawn. $\ell$ intersects $k$ at the points $B$ and $C$ ($C$ is between $F$ and $B$). The tangent to the circle $k$ at the point $C$ intersects the line segment $FA$ at the point $E$. $FX$ is a bisector of the triangle $AFC$. If the points $E,X$ and $B$ are collinear, prove that the product of two side lengths of the triangle $ABC$ equals to the square of the third side length.
Fig. 31
Fig. 31