Problem

Source: Iranian National Olympiad (3rd Round) 2008

Tags: geometry, circumcircle, power of a point, radical axis, geometry proposed



Let $ ABC$ be an isosceles triangle with $ AB=AC$, and $ D$ be midpoint of $ BC$, and $ E$ be foot of altitude from $ C$. Let $ H$ be orthocenter of $ ABC$ and $ N$ be midpoint of $ CE$. $ AN$ intersects with circumcircle of triangle $ ABC$ at $ K$. The tangent from $ C$ to circumcircle of $ ABC$ intersects with $ AD$ at $ F$. Suppose that radical axis of circumcircles of $ CHA$ and $ CKF$ is $ BC$. Find $ \angle BAC$.