Three girls Reshma,Salma,and Mandip are playi | vedclass

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(B) Let the positions of Reshma,Salma,and Mandip be $R, S,$ and $M$ respectively on the circle with center $O$ and radius $5 \, m$.Given $RS = SM = 6

Vedclass · Accepted Answer

$9.6$

Vedclass · Answer

(B) Let the positions of Reshma,Salma,and Mandip be $R, S,$ and $M$ respectively on the circle with center $O$ and radius $5 \, m$.Given $RS = SM = 6 \, m$.Since equal chords subtend equal angles at the center,$\angle ROS = \angle SOM$.Let $OP$ be the perpendicular from $O$ to $RM$,intersecting $RM$ at $P$ and $OS$ at $K$.Since $RS = SM$,$OS$ is the perpendicular bisector of $RM$. Thus,$RM \perp OS$ and $RP = PM$.Let $OK = x$. Then $KS = 5 - x$.In $\Delta ORK$,$RK^2 = OR^2 - OK^2 = 5^2 - x^2 = 25 - x^2$.In $\Delta RSK$,$RK^2 = RS^2 - KS^2 = 6^2 - (5 - x)^2 = 36 - (25 - 10x + x^2) = 11 + 10x - x^2$.Equating the two expressions for $RK^2$: $25 - x^2 = 11 + 10x - x^2$.$10x = 14 \Rightarrow x = 1.4 \, m$.Now,$RK^2 = 25 - (1.4)^2 = 25 - 1.96 = 23.04$.$RK = \sqrt{23.04} = 4.8 \, m$.Since $RM = 2 	imes RK$,$RM = 2 	imes 4.8 = 9.6 \, m$.

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