Problem

Source: The South African Mathematical Olympiad Third Round 2023 P6

Tags: geometry, rectangle



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(i.e., the three lines intersect in one point).