RU-ALLRUSSIAN 1976 Problem 3

(1) The circles $\mathrm{C_1}$ , $\mathrm{C_2}$ , $\mathrm{C_3}$ with equal radius all pass through the point X. $\mathrm{C_i}$ and $\mathrm{C_j}$ also intersect at the point $\mathrm{Y_{ij}}$ . Show that angle $\mathrm{XO_1Y_{12} + angle XO_2Y_{23} + angle XO_3Y_{31} = 180 deg}$ where $\mathrm{O_i}$ is the center of circle $\mathrm{C_i}$ .