Question 26
Let $ABC$ be a triangle with $\widehat{BAC}=60^{\circ}$ and let $\Gamma$ be its circumcircle. Let $H$ be the orthocenter of $ABC$ and $S$ the midpoint of the arc $\widehat{BC}$ not containing $A$. Let $P$ be the point of $\Gamma$ such that $\widehat{SPH}=90^{\circ}$. Show that there exists a circle passing through $P, S$ which is tangent to $(AB)$ and $(AC)$.