**Circles ncert solutions Chapter 10 Exercise 10.2 Question 8**

**8. ** A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

**Solution:**

ABCD is a quadrilateral. All the sides of quadrilateral are tangents to the circle.

Therefore, DC, CB, AB and AD are tangents to the circle.

CR = CQ {Two Tangents drawn from an external point to the circle are equal} ** (1)**

AP=AS {Two Tangents drawn from an external point to the circle are equal} **(2)**

PB=BQ {Two Tangents drawn from an external point to the circle are equal} ** (3)**

DR = DS {Two Tangents drawn from an external point to the circle are equal} **(4)**

Adding **(1), (2), (3), and (4), we get**

**Hence Proved**