Please solve question no.1.

Dear Student,
Let L and N be the foot of the perpendiculars from P and Q to ACB.


PL,MC and QN are parallel lines and make equal intercepts on line PQ.

Like wise, the intercepts on line ACB will also be equal.

NC=CL

But L and N are foot of perpendiculars from centers of circles to the corresponding chords .
So L and N bisect chords AC and CB. Hence  AC=BC
Regards