Question

Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of a radius 5cm drawn in the park. Reshma throws a ball to Salma, Salma to Mandeep, Mandeep to Sharma. If the distance between Salma and Reshma, and between Salma and Mandeep is 6cm 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 $△ORS=\frac{1}{2}\times OA\times RS$

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

$RC\times 5=24$

$RC=4.8$

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

So, distance between Reshma and Mandip is 9.6 m.