Q14 of 105 Page 612

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


Let us consider a circle with center O and BC be a chord, and AB and AC are tangents drawn at end of a chord


To Prove : AB and AC make equal angles with chord, i.e. ∠ABC = ∠ACB


Proof :


In △ABC


AB = PC


[Tangents drawn from an external point to a circle are equal]


∠ACB = ∠ABC


[Angles opposite to equal sides are equal]


Hence Proved.


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