Question 86
Two squares with the centers $C_1$ and $B_1$ are constructed on the sides $AB$ and $AC$ outside of the acute-angled triangle $ABC$, respectively. The square $C_1B_1DE$ is constructed on the segment $C_1B_1$ so that $A$ and $D$ lie in the different half-planes with respect to $C_1B_1$.
Prove that the center of the square $C_1B_1DE$ belongs to the line $BC$.
Prove that the center of the square $C_1B_1DE$ belongs to the line $BC$.