Question 123
Two circles $\omega_1$ and $\omega_2$ intersect at $P$ and $K$. $XY$ is the common tangent of them near to $P$ such that $X$ is on $\omega_1$ and $Y$ is on $\omega_2$. $XP$ intersects $\omega_2$ for the second time at $C$, and $YP$ intersects $\omega_1$ for the second time at $B$. $A$ is the intersection of $BX$ and $CY$. If $Q$ be the second intersection point of circumcircle $ABC$ and circumcircle $AXY$, prove that
$$
\overline{QXA} = \overline{QKP}
$$
$$
\overline{QXA} = \overline{QKP}
$$