Question 143
Two circles $C_1,C_2$ of radii $r_1,r_2$ intersect at $A,B$. A variable line through $B$ meets $C_1,C_2$ again at $P_r,Q_r$, respectively.
Prove that there is a point $M$, depending only on $C_1,C_2$, such that the perpendicular bisector of $P_rQ_r$ passes through $M$.
Prove that there is a point $M$, depending only on $C_1,C_2$, such that the perpendicular bisector of $P_rQ_r$ passes through $M$.