Post Number:#1 by Thamim Zahin » Tue Jan 10, 2017 4:09 pm
5. Let the circles $w$ and $w'$ intersect in points $A$ and $B$. Tangent to circle $w$ at $A$ intersects $w'$ in $C$ and tangent to circle $w'$ at $A$ intersects $w$ in $D$. Suppose that the internal bisector of $\angle CAD$ intersects $w$ and $w'$ at $E$ and $F$, respectively, and the external bisector of $\angle CAD$ intersects $w$ and $w'$ in $X$ and $Y$, respectively. Prove that the perpendicular bisector of $XY$ is tangent to the circumcircle of triangle $BEF$.