Question 18
Let $ABC$ be a right triangle in $A$, with $AB \gt AC$; let $AH$ be the height relative to the hypotenuse. On the straight line $BC$ take $D$ such that $H$ is the midpoint of $BD$; then let $E$ be the foot of the perpendicular conducted from $C$ to $AD$. Prove that $EH = AH$.