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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?


A
4.8 m
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B
9.6 m
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C
2.4 m
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D
7.2 m
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Solution

The correct option is

B

9.6 m



We draw SNRS.


Now, SN bisects RM and also SN (produced) passes through the centre O.

Put RN=x

The Ar.(ΔORS)=12×OS×RN

=12×5×x (OS=OR=5m)

i.e., Ar.(ΔORS)=52x .....(1)

Now, draw OPRS,P is the mid-point of RS.

PR=PS=3 m

OP2=(5)2(3)2=16

OP=4 m

Here, Ar.(ΔORS)=12×RS×OP=12×6×4 i.e., Ar.(ΔORS)=12m2

From (1) and (2), we have

52x=12

x=4.8 m

RM=2x=2×4.8 m

RM=9.6 m

Thus, distance between Reshma and Mandip is 9.6 m.

Hence, option B is the correct answer.



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