Santa decorates his Christmas tree with a triangular decoration. Suppose the triangular decoration can be represented by $\vartriangle ABC$. Let $\omega$ be its incircle and $\omega_A$, $\omega_B$, $\omega_C$ be its $A$-, $B$-, $C$-excircles respectively. Let $J_A$, $J_B$, $J_C$ be the A-, $B$-, $C$-excentres of $\vartriangle ABC$ respectively. $X$ is the radical centre of $\omega$, $\omega_B$, $\omega_C$. $Y$ is the radical centre of $\omega$, $\omega_C$, $\omega_A$. $Z$ is the radical centre of $\omega$, $\omega_A$, $\omega_B$. Prove that $XJ_A$, $Y J_B$, $ZJ_C$ are concurrent