Question 101
A square with center $A_{1}$ is inscribed in an acute triangle $A B C$ in such a way that two corners lie on $B C$ and one each on $A B$ or $A C$. The squares are defined analogously with the centers $B_{1}$ and $C_{1}$.
Prove that the lines $A A_{1}, B B_{1}$ and $C C_{1}$ have a common intersection.
Prove that the lines $A A_{1}, B B_{1}$ and $C C_{1}$ have a common intersection.