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 6m each, what is the distance between Reshma and Mandip?

Answer 1

Draw perpendiculars OA and OB on RS and SM, respectively.

AR = AS = `6/2` = 3m

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

In ΔOAR,

OA² + AR² = OR²

OA² + (3m)² = (5m)²

OA² = (25 − 9) m² = 16m²

OA = 4m

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 isosceles triangles is bisected by another diagonal.

∴ ∠RCS will be of 90° and RC = CM

Area of ΔORS = `1/2 xx OA xx RS`

`1/2 xx RC xx OS` = `1/2 xx 4 xx 6`

Rc × 5 = 24

RC = 4.8

RM = 2RC

RM = 2(4.8)

RM = 9.6

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