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 perpendiculars OA and OB on RS and SM respectively.

OR = OS = OM = 5 m. (Radii of the circle)

In ΔOAR,

OA² + AR² = OR²

OA² + (3 m)² = (5 m)²

OA² = (25 − 9) m² = 16 m²

OA = 4 m

ORSM will be a kite (OR = OM and RS = SM). We know that the diagonals of a kite are perpendicular and the diagonal common to both the isosceles triangles is bisected by another diagonal.

∴∠RCS will be of 90° and RC = CM

Area of ΔORS =

Therefore, the distance between Reshma and Mandip is 9.6 m.