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

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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?

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Let Reshma, Salma and Mandip be represented by R, S and M respectively.

Draw OL ⊥ RS,

OL2 = OR2 – RL2

OL2 = 52 – 32 [RL = 3 m, because OL ⊥ RS]

= 25 – 9 = 16

OL = 16 = 4 Now, area of triangle ORS = 1/ 2 × KR × 05

= 1/ 2 × KR × 05

Also, area of ∆ORS = 1/ 2 × RS × OL = 1/ 2 × 6 × 4 = 12 m

⇒ 1/ 2 × KR × 5 = 12

⇒ KR = 12x 2/ 5 =24/ 5 = 4.8 m

⇒ RM = 2KR

⇒ RM = 2 × 4.8 = 9.6 m

Hence, distance between Reshma and Mandip is 9.6 m Ans.

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