# Geometry Kings, Solve This!

Geometry Level 5

Let the excircle of the triangle $$ABC$$ lying opposite to $$A$$ touch its side $$BC$$ at the point $$A_{1}$$. Define the points $$B_{1}$$ and $$C_{1}$$ analogously. Suppose that the circumcentre of the triangle $$A_{1}B_{1}C_{1}$$ lies on the circumcircle of the triangle $$ABC$$. Find the measure of the largest angle in triangle $$ABC$$ in degrees.

×