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Question
Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20 m drawn in a park. Ishita throws a ball o Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is 24 m each, what is the distance between Ishita and Nisha.
Solution
Let R, S and M be the position of Ishita, Isha and Nasha respectively
`AR=AS=24/2=12cm`
`OR=OS=OM=20m`
In OAR
`OA^2+AR^2=OR^2`
`OA^2+ (112m^2)=(20m)^2`
`OD^2=(400-144)m^2=256m^2`
`OA=16m`
WKT, in an isosceles triangle altitude divides the base, So in ΔRSM ∠ RCS will be `90°` and
RC=CM.
Area of ΔORS =`1/2xxOAxxRS`
⇒`1/2xxRCxxOS=1/2xx16xx24`
⇒`RCxx20=16xx24⇒RC=192⇒RM=2(192)=38.4m`
So, distance between ishita and Nisha is `384m`.
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