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.

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