梅涅老四证明题

Circles $O_1$and $O_2$ are both tangent to the lines containing the three sides of $\mathrm{△}ABC$. Let $E$, $F$, $G$, and $H$ be the points of tangency. The lines $EG$and $FH$ intersect at point $P$. Prove that $PA\perp BC$.