Question 2
Let $ABC$ be an isosceles triangle with $AB=AC$. A point $O$ varies on the line $BC$, subject to the condition that the circle with center $O$ and radius $OA$ has neither $AB$ nor $AC$ as a tangent. The lines $AB,AC$ meet the circle again at $M,N$, respectively. Determine the locus of the orthocenter of triangle $AMN$.