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?
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(S−a)(S−b)(S−c)
⇒△=√32 m(32 m−24 m)(32 m−20 m)(32 m−20 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.
⇒OK⊥RM and RK⊥OS.
Let RK=x
Now, ar(ΔORS)=12×base×altitude
=12×OS×RK
⇒12×20×x=10x
∴ 10x=192 m2⇒x=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.