Question 113
$\triangle ABC$ is an acute triangle. Let $A_1$ be the centre of the square inscribed in $\triangle ABC$ having two vertices on side $BC$. Let $B_1$ be the centre of the square inscribed in $\triangle ABC$ having two vertices on side $CA$. Let $C_1$ be the centre of the square inscribed in $\triangle ABC$ having two vertices on side $AB$. Prove that lines $AA_1$, $BB_1$ and $CC_1$ are concurrent.