**Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?**

**Solution:**

Let R, S and M are the points representing Reshma, Salma and Mandeep respectively. Let O be the centre of the circle. Join R, S and M with the centre of the circle.

It is given that RS = MS = 6 m

And Radius of circle = OR = OM = OS **= 5 m**

Let's draw

RQ=QS **(Perpendicular from the centre to a chord bisects the chord)**

m

In , using Pythagoras theorem, we can say that

**m**

In and , we have

**(Radii of circle)**

** (given)**

** (Commom)**

Therefore, **by SSS congruence rul**e, we have

** (Corresponding parts of congruent triangles are equal) (1)**

Now in and , we have

**(Common)**

** (Proved above in (1))**

**(given)**

Therefore, **by SAS congruence rule**, we have

**(2)**

But, we also have **(Linear pair) (3)**

From **(2)** and **(3)**, we have

Similarly,

Hence, ** (Perpendicular from the centre to a chord bisects the chord) (4)**

Now, Area of

m

We get m

Putting this in **(4)**, we get **m**

** m**