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?

First, we have to draw, OA ⊥ RS and OB ⊥ SM

AR = AS = = 3 cm (because, perpendicular drawn from the centre to a chord, divides the chord into equal parts.)



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

In ΔOAR,

⇒ OA2 + AR2 = OR2

⇒ OA2 + (3m)2 = (5m)2

⇒ OA2 = (25 − 9) m2 = 16m2

⇒ 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 = 90° and RC = CM

Area of ΔORS can be written in two ways. 

(i)  ½ × OA× RS and (ii) ½ × RC × OS

∴ ½ × RC × OS = ½ × OA × RS

⇒ ½ × RC × OS = ½ × 4 × 6

⇒ RC × 5 = 24

⇒ RC = 4.8 m

Now, RM = 2 × (RC)

= 2 × 4.8 = 9.6

Therefore, the distance between Reshma and Mandip is 9.6 m


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