KöMaL 2009 C1004

An arbitrary line is drawn through vertex $A$ of a square ABCD , and perpendiculars are dropped onto the line from the vertices $B$ and $D$. The feet of the perpendiculars are $B_1$ and $D_1$, respectively. Prove that $AB_1 ^2$+$AD_1 ^2$=$BB_1 ^2$+$DD_1 ^2$.