**Circles ncert solutions Chapter 10 Exercise 10.2 Question 10**

**10.** Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the center.

**Solution:**

** Given:** AB and AC are two tangents to a circle.

**To Prove: **

**Proof: **

{Tangent is perpendicular to the radius of circle} **(1)**

{Tangent is perpendicular to the radius of circle} **(2)**

Also,

** {Sum of interior angles of quadrilateral is equal to }**

Putting **(1)** and **(2)** in the above equation, we get

**Hence Proved**