Q. 93.9( 17 Votes )
Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
Let QR be a chord in a circle with center O and ∠1 and ∠2 are the angles made by tangent at point R and Q with chord respectively.
To Prove : ∠1 = ∠2
Let P be another point on the circle, then, join PQ and PR.
Since, at point Q, there is a tangent.
∠RPQ = ∠2 [angles in alternate segments are equal] [Eqn 1]
Since, at point R, there is a tangent.
∠RPQ = ∠1 [angles in alternate segments are equal] [Eqn 2]
From Eqn 1 and Eqn 2
∠1 = ∠2
Hence Proved .
Rate this question :