IGO 2016 Medium/5

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IGO 2016 Medium/5

Post Number:#1  Unread postby 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 $BEF$.
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Thamim Zahin
 
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