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

PT is the tangent to CBSE 10th Board


Let’s starts from LHS:

PA . PB = (PC – AC) (PC + BC)

Given that PC is \perp 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

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