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# Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius $ 5 \mathrm{~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 \mathrm{~m} $ each, what is the distance between Reshma and Mandip?

"

Given:

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius \( 5 \mathrm{~m} \) drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. The distance between Reshma and Salma and between Salma and Mandip is \( 6 \mathrm{~m} \) each.

To do:

We have to find the distance between Reshma and Mandip.

Solution:

Let $R, S$ and $M$ be the positions of Reshma, Salma, and Mandip respectively. Draw perpendicular $OA$ and $OB$ on $RS$ and $SM$ respectively.

$AR=AS= \frac{6}{2} =3\ m$

$OR=OS=OM=5\ m$ [Radii of the circle]

In $\triangle OAR$

$OA^2 + AR^2 = OR^2$

$OA^2 + 3^2 = 5^2$

$OA^2= 25−9$

$OA^2=16$

$OA=4\ m$

We know that,

In an isosceles triangle, altitude divides the base.

So, in $\triangle RSM$

$\angle RCS=90^o$

$RC=CM$

Area of $\triangle ORS= \frac{1}{2} \times OA \times RS$

$\frac{1}{2} \times RC \times OS= \frac{1}{2}\times4\times6$

$RC\times 5=24$

$RC=4.8\ m$

$RM=2RC=2\times4.8=9.6\ m$

So, the distance between Reshma and Mandip is $9.6\ m$.

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