KöMaL 2024 B5385

Let $F$ denote the center of the nine-point circle of acute triangle $ABC$. Prove that $AF^2-BF^2=Rc\sin(\beta-\alpha)$, where $R$ denotes the radius of the circumcircle, $c$ denotes the length of side $AB$, and $\alpha$ and $\beta$ denote the interior angles at $A$ and $B$.