Question 140
Circles $\omega_{1}$, $\omega_{2}$, and $\omega_{3}$ are centered at $M$, $N$, and $O$, respectively. The points of tangency between $\omega_{2}$ and $\omega_{3}$, $\omega_{3}$ and $\omega_{1}$, and $\omega_{1}$ and $\omega_{2}$ are tangent at $A$, $B$, and $C$, respectively. Line $MO$ intersects $\omega_{3}$ and $\omega_{1}$ again at $P$ and $Q$ respectively, and line $AP$ intersects $\omega_{2}$ again at $R$. Given that $ABC$ is an equilateral triangle of side length $1$, compute the area of $PQR$.