Question

Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m 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.

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

AR=AS=26=3 cm

OR=OS=OM=5 m   [radii of circle]

In △OAR

OA2+AR2=OR2

OA2+32=52

OA=25−9

OA=4 m

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

So, in △RSM

∠RCS=90o

RC=CM

Area of △ORS=21×OA×RS

21×RC×OS=21×4×6

RC×5=24

RC=4.8 m

RM=2RC=2×4.8=9.6 m

So, distance between Reshma and Mandip is 9.6 m