Circles ncert solutions Chapter 10 Exercise 10.2 Question 5
5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center.
We can prove this by the method of contradiction.
Suppose OP is the radius of circle and perpendicular (O'P) at the point of contact to the tangent does not pass through center. (1)
We know that radius of the circle is perpendicular to the tangent at the point of contact. Therefore, . (2)
(1) and (2) are contradicting with each other. Both (1) and (2) can be true only if point O' lies on point O. Therefore, our supposition was wrong in the beginning.
Hence, Perpendicular (O'P) at the point of contact to the tangent passes through center.