Q. 144.7( 7 Votes )

# 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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