Two side-by-side squares are inscribed in a semicircle. The diameter of the semicircle is $16$. What is the sum of the two squares' areas?
This is a bonus question from my online math class that I've been trying to solve but haven't gotten very far. I named $CD$ $x$ and $HD$ $y$, then drew $OB$ and $OF$, then did the Pythagorean theorem to try to get $x^2+y^2$ but I didn't have much luck with that.