Question

Prove that the tangents drawn at the endpoints of a chord of a circle make equal angles with chord

Answer 1

Consider two triangles ΔAPR and ΔAQR
the sides AP = AQ ( as because tangents drawn from an internal point to a circle are equal]
The angles ∠PAR and ∠QAR are equal
AR = AR [Common side]
∴ ΔAPR ≅ ΔAQR (using side angle side congruency.)
Hence ∠APR = ∠AQR (hence proved)

Answer 2

FIGURE IS IN THE ATTACHMENT
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]
HOPE THIS WILL HELP YOU....