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?

Answer 1

Draw perpendicular OA and OB on RS and SM respectively

$AR=AS=\frac{1}{6}=3m$
$OR=OS=OM=5m.$ (Radii of the circle) In
$O{A}^2+A{R}^2=O{R}^{2}O{A}^1+\left(3m^2\right)=(5m{)}^{2}O{A}^2=(25-9)m^2=16m^{2}OA=4m$
ORSM will be a kite (OR = OM and RS = SM). We know that diagonals of a kite are perpendicular and the diagonal common to both the isosceles traingle is bisected by another diagonal
$\therefore \angle RCS$ will be of ${90}^{\circ }andRC=CM$
Area of $\Delta ORS=\frac{1}{2}\times OA\times RS\frac{1}{2}\times RC\times OS=\frac{1}{2}\times 4\times 6$
$RC\times 5=24RC=4.8RM=2RC=2\left(4.8\right)=9.6$
Therefore, the distance between Reshma and Mandip is 9.6 m.