Question

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 $6$ m each, what is the distance between Reshma and Mandip?

• A. $4.8$ m
• B. $9.6$ m
• C. $2.4$ m
• D. $7.2$ m

Answer 1

The correct option is

B

$9.6$ m

We draw $SN\perp RS$.

Now, $SN$ bisects $RM$ and also $SN$ (produced) passes through the centre $O$.

Put $RN=x$

The $Ar.\left(\Delta ORS\right)=\frac{1}{2}\times OS\times RN$

$=\frac{1}{2}\times 5\times x$ ($\because OS=OR=5m$)

i.e., $Ar.\left(\Delta ORS\right)=\frac{5}{2}x$ .....(1)

Now, draw $OP\perp RS,P$ is the mid-point of $RS$.

$\Rightarrow PR=PS=3$ m

$\Rightarrow O{P}^2=(5{)}^2-(3{)}^2=16$

$\Rightarrow OP=4$ m

Here, $Ar.\left(\Delta ORS\right)=\frac{1}{2}\times RS\times OP=\frac{1}{2}\times 6\times 4$ i.e., $Ar.\left(\Delta ORS\right)=12m^2$

From (1) and (2), we have

$\frac{5}{2}x=12$

$\Rightarrow x=4.8$ m

$\Rightarrow RM=2x=2\times 4.8$ m

$\Rightarrow RM=9.6$ m

Thus, distance between Reshma and Mandip is $9.6$ m.

Hence, option B is the correct answer.