Let $a_1,b_1,c_1$ are three lines each two of them are mutually crossed and aren't parallel to some plane. The lines $a_2,b_2,c_2$ intersect the lines $a_1,b_1,c_1$ at the points $a_2$ in $A$, $C_2$, $B_1$; $b_2$ in $C_1$, $B$, $A_2$; $c_2$ in $B_2$, $A_1$, $C$ respectively in such a way that $A$ is the perpendicular bisector of $B_1C_2$, $B$ is the perpendicular bisector of $C_1A_2$ and $C$ is the perpendicular bisector of $A_1B_2$. Prove that: (a) $A$ is the perpendicular bisector of $B_2C_1$, $B$ is the perpendicular bisector of $C_2A_1$ and $C$ is the perpendicular bisector of $A_2B_1$; (b) triangles $A_1B_1C_1$ and $A_2B_2C_2$ are the same.