SMO 2001 Problem 1

In a parallelogram $ABCD$ , the perpendiculars from $A$ to $BC$ and $CD$ meet the line segments $BC$ and $CD$ at the points $E$ and $F$ respectively. Suppose $AC = 37$ cm and $EF = 35$ cm. Let $H$ be the orthocentre of $\vartriangle AEF$ . Find the length of $AH$ in cm. Show the steps in your calculations.