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5. 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, and 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 :

Let O be the centre of the circle and Reshma, Salma and Mandip are represented by the points R, S and M, respectively. Let RP = x m.
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Area of \(\triangle{ORS}\) = 1/2 × x × 5 = 5x/2 ...(i)(Since, in \(\triangle{ORM}\), RM is a chord therefore \(OP\perp{RM}\))
In right angled triangle \(\triangle{RON}\), \({OR}^2 = {RN}^2 + {NO}^2\)
i.e., \({5}^2 = {3}^2 + {NO}^2\)
i.e., \({NO}^2 = 25 - 9 = 16\)
Thus, NO = 4cm
So, Area of \(\triangle{ORS}\) = 1/2 × RS × ON = 1/2 × 6 × 4 = 12 ...(ii)

From Equations (i) and (ii), we get,
5x/2 = 12
Therefore, x = 24/5.
Since, P is the mid- Point of RM,
Thus, RM = 2RP = 2 × 24/5
i.e., RM = 48/5 = 9.6m
Hence, the distance between Reshma and Mandip is 9.6m.