Question 98
In an acute triangle $ABC$ with $AC \gt AB$ let $D$ be the projection of $A$ on $BC$, let $E$ and $F$ be the projections of $D$ on $AB$ and $AC$ and let $G$ and $H$ be the second intersections of the line $AD$ with $EF$ and the circumcircle of triangle $ABC$. Prove
$$
AG \cdot AH = AD^2.
$$
$$
AG \cdot AH = AD^2.
$$