Question

prove that tangents drawn at the points of circle make an equal angle with chord

Answer 1

Answer:

Step-by-step explanation:

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.