**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.**

**Solution:**

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.**