Question 78
Let $ABC$ be an isosceles triangle with $AB = AC = 5$. Let $D$ be a point on side $AB$ satisfying $AD = 3$, and let $E$ be a point on side $BC$ (excluding the endpoints $B$ and $C$). Let $\omega$ be the circle passing through $E$ and tangent to line $AB$ at $B$. Suppose that $\omega$ is tangent to the circumcircle of triangle $ADE$. Let $F$ be the intersection point of $\omega$ and line $AE$, other than $E$. When $CF = 10$, find the length of side $BC$.