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