Question

prove that the tangents drawn at the end points of a chord of a circle make equal angle with the chord

Answer 1

Step-by-step explanation:

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 = ∠PBC

Proof : In ΔPAC and ΔPBC

PA = 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]