Q) PT is the tangent to the circle centered at O. OC is Perpendicular to the chord AB. Prove that PA.PB = PC²-AC².

Ans:

Let’s starts from LHS:

PA . PB = (PC – AC) (PC + BC)

Given that PC is to chord AB, therefore it bisects chord AB (by circle’s property)

Hence, AC = BC

Therefore LHS:

PA. PB = (PC – AC) (PC + AC)

= PC² – AC²  =  RHS

Hence Proved