Question 63
Two circles $\omega_1$ and $\omega_2$ intersect each other at points $X$ and $Y$. Two lines pass through $Y$: one intersects $\omega_1$ and $\omega_2$ for the second time at points $A$ and $B$ respectively and another intersects $\omega_1$ and $\omega_2$ for the second time at points $C$ and $D$ respectively. The line $AD$ intersects $\omega_1$ and $\omega_2$ for the second time at points $P$ and $Q$ respectively such that $YP = YQ$.
Prove that circumcircles of $\triangle BCY$ and $\triangle PQY$ touch each other.
(Palina Chernikava)
Prove that circumcircles of $\triangle BCY$ and $\triangle PQY$ touch each other.
(Palina Chernikava)