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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 to 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?

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Solution

Since, Distance between Isha and Ishita and Ishita and Nisha is same.


RS=SM=24 m

and OS=20 m [Since, radius of the circle]

Now, in ORS

Let RS=a=24 m

OS=b=20 m

and OR=c=20 m

S=a+b+c2=20 m+20 m+24 m2

S=32 m

Area of triangle =S(Sa)(Sb)(Sc)

=32 m(32 m24 m)(32 m20 m)(32 m20 m)

=32 m(8 m)(12 m)(12 m)

=4×8×8×12×12 m2

=2×8×12 m2

=192 m2...(i)

In radius OS perpendicularly bisects the chord RM.

OKRM and RKOS.

Let RK=x

Now, ar(ΔORS)=12×base×altitude

=12×OS×RK

12×20×x=10x

10x=192 m2x=19210=19.2 m [From (i)]

Now RM=2×RK=2x

=2×19.2 m=38.4 m

Hence distance between Ishita and Nisha is 38.4 m.


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