Q21 of 52 Page 10

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord. (CBSE 2017)


Consider a circle, In which, PQ is a chord and AP and AQ are two tangents drawn at end points P and Q of the chord.


To Prove: tangent make equal angles with the chord i.e. ∠AQP = ∠APQ


As we know, tangents drawn from an external point are equal


⇒ AP = AQ [Tangents from common external point A]


⇒ ∠AQP = ∠APQ [Angles opposite to equal sides are equal]


Hence, Proved !

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