Question

If a point P lies in the exterior of a circle with centre O and radius 3 cm, then the line segment:

Answer 1

Answer:

(i) PA . PB = (PN – AN) (PN + BN) = (PN – AN) (PN + AN) (As AN = BN) = PN2 – AN2 (ii) PN2 – AN2 = (OP2 – ON2) – AN2 (As ON⊥PN) = OP2 – (ON2 + AN2) = OP2 – OA2 (As ON⊥AN) = OP2 – OT2 (As OA = OT) (iii) From (i) and (ii) PA.PB = OP2 – OT2 = PT2 (As ∠OTP = 90°)Read more on Sarthaks.com - https://www.sarthaks.com/123723/in-fig-from-an-external-point-tangent-pt-and-line-segment-pab-is-drawn-to-circle-with-centre