Question 135
In the plane, let be given an isosceles triangle $ABC$ ($AB = AC$). A variable circle $(O)$ with center $O$ on the line $BC$, passes through $A$ but does not touch the lines $AB$, $AC$. Let $M$, $N$ be respectively the second points of intersection of the circle $(O)$ with the lines $AB$, $AC$. Find the locus of the orthocenter of triangle $AMN$.