ShortAISWU2 & 4 MarksQ. 1. Show that the tangents drawn at theend points of a chord of the circle make equaln angles with the chord.(U. P. 2007, 11)tSolution. Given : AB is a chord of circleeiniC(0, r) and AP and BQ are the tangents.

ShortAISWU2 & 4 MarksQ. 1. Show that the tangents drawn at theend poin

1.	ShortAISWU2 & 4 MarksQ. 1. Show that the tangents drawn at theend points of a chord of the circle make equaln angles with the chord.(U. P. 2007, 11)tSolution. Given : AB is a chord of circleeiniC(0, r) and AP and BQ are the tangents.
Answer» Let AB be a chord of a circle with center O and let AP and BP be the tangents at A and B.Let the tangent meet at P.Join OP Suppose OP meets AB at C.To prove : ∠PAC = ∠PBCProof : In ΔPAC and ΔPBCPA = PB [Tangents from an external point to a circle are equal]∠APC = ∠BPC [PA and PB are equally inclined to OP]PC = PC [Common]ΔPAC ≅ ΔPBC [SAS Congruence]∠PAC = ∠PBC [C.P.C.T]