Question 47
Let $ABIH$, $BDEC$, and $ACFG$ be arbitrary rectangles constructed (externally) on the sides of triangle $ABC$. Choose point $S$ outside rectangle $ABIH$ (on the opposite side as triangle $ABC$) such that $\angle SHI = \angle FAC$ and $\angle HIS = \angle EBC$. Prove that the lines $FI$, $EH$, and $CS$ are concurrent.