Question 16
The circles $C_1$, $C_2$, $C_3$ with equal radius all pass through the point $X$. $C_i$ and $C_j$ also intersect at the point $Y_{ij}$. Show that $\angle X O_1 Y_{12} + \angle X O_2 Y_{23} + \angle X O_3 Y_{31} = 180^\circ$ where $O_i$ is the center of circle $C_i$.