Question

if pa and pb are are two tangents drawn from a point p to a circle with centre o touching it at a and b prove that op is the perpendicular bisector of ab

Answer 1

In triangles PAC &PBC

PA=PB

angle APC=angle BPC

PC=PC

triangle PAC congruent triangle PBC [BY SAS]

=> AC=BC &  angle ACP= angle BCP [CPCT]

bt, angle ACP+ angle BCP= 180 deg.

.`. angle ACP= angle BCP=90 deg.

Hence, OP is the perpendicular bisector of AB