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prove that the tangent drawn from the endpoint of the chord of a circle make equal angle with chord ,

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Answered by Anonymous
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Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.


Let NM be a chord of a circle with centre C.

Let tangents at M and N meet at the point O.

Since OM is a tangent, OM CM, i.e., OMC = 90°

Since ON is a tangent, ON CN, i.e., ONC = 90°

In DCMN,

CM = CN (Radius of the same circle)

CMN = CNM

Now, OMC = ONC

OMC - CMN = ONC - CNM

OML = ONL

Thus, tangents make equal angles with the chord.
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