Question 120
Two circles of respective centers $B$ and $C$ and different radii are tangent externally at a point $A$. Let $t$ be a tangent common to the two circles not containing the point $A$. The perpendicular to the line $t$ passing through the point $A$ cuts the perpendicular bisector of the segment $[BC]$ at a point $F$. Show that $BC = 2AF$. 