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.

Answer :

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 .


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