**Circles ncert solutions Chapter 10 Exercise 10.2 Question 11**

**11.** Prove that the parallelogram circumscribing a circle is a rhombus.

**Solution:**

**Given:** PQRS is a parallelogram circumscribing a circle.

**To Prove:** PQRS is a rhombus

**Proof:**

**Note:** **A parallelogram with all equal sides is rhombus. Therefore, if we can prove that all the sides of PQRS are equal then it means its a rhombus.**

PQ =SR and QR = SP ** {Opposite sides of parallelogram are equal} (1)**

AP = PB **(2)**

CQ=BQ ** (3)**

RC=RD **(4)**

AS = SD **(5)**

Adding **(2), (3), (4) and (5), we get**

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

**(6)**

From **(1)** and **(6)**, we can say that

**which means PQRS is a rhombus.**

**Hence Proved**