Question 39
$ABC$ is a right triangle with $\angle A = 30^{\circ}$ and circumcircle $O$. Circles $\omega_1$, $\omega_2$, and $\omega_3$ lie outside $ABC$ and are tangent to $O$ at $T_1$, $T_2$, and $T_3$ respectively and to $AB$, $BC$, and $CA$ at $S_1$, $S_2$, and $S_3$, respectively. Lines $T_1 S_1$, $T_2 S_2$, and $T_3 S_3$ intersect $O$ again at $A'$, $B'$, and $C'$, respectively. What is the ratio of the area of $A'B'C'$ to the area of $ABC$?