Question

PA and PB are tangents from P to the circle with centre O. At M, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN.

Answer 1

KA = KM ---(1) {Length of tangents drawn from an external point to a  circle are equal }

NM = NB

KN = KM + MN

KN = KA+ BM            {Using (1)}