Question

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

Answer 1

Draw perpendicular OA and OB on RS and SM respectively.

Let R,S and M be the position of Reshma, Salma and Mandip respectively.

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

$OR=OS=OM=5m$ [radii of circle]

In $△OAR$

$O{A}^2+A{R}^2=O{R}^2$

$O{A}^2+3^2=5^2$

$OA=\sqrt{25-9}$

$OA=4m$

We know that in an isosceles triangle altitude divides the base ,

So, in $△RSM$

$\angle RCS={90}^o$

$RC=CM$

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

$\frac{1}{2}\times RC\times OS=\frac{1}{2}\times 4\times 6$

$RC\times 5=24$

$RC=4.8m$

$RM=2RC=2\times 4.8=9.6m$

So, distance between Reshma and Mandip is$9.6m$