Question 137
Let $ABC$ be an acute, non-isosceles triangle, $AX$, $BY$, $CZ$ are the altitudes with $X$, $Y$, $Z$ belonging to $BC$, $CA$, $AB$ respectively. Respectively denote $(O_{1})$, $(O_{2})$, $(O_{3})$ as the circumcircles of triangles $AYZ$, $BZX$, $CXY$. Suppose that $(K)$ is a circle that is internally tangent to $\left(O_{1}\right)$, $\left(O_{2}\right)$, $\left(O_{3}\right)$. Prove that $(K)$ is tangent to the circumcircle of triangle $ABC$.