Question 29
Let $A_{1}, B_{1}, C_{1}$ be the points on the sides $BC, CA, AB$ (respectively) of the triangle $ABC$. Prove that the three circles circumscribed about the triangles $\triangle AB_{1}C_{1}$, $\triangle BC_{1}A_{1}$, and $\triangle CA_{1}B_{1}$ intersect at one point.