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 distance between Ishita and Nisha?

Question

Philoid · Accepted Answer

Let R, S and M be the position of Ishita, Isha and Nisha respectively

AB = AS = = 12 cm

OR = OS = OM = 20 m (Radii of circle)

In

OA² + AR² = OR²

OA² + (12 m)² = (20 m)²

OA = (400 – 144) m²

= 256 m²

= 16 m

We know that,

In an isosceles triangle altitude divides the base.

So, in ,

∠RCS = 90^o

And,

RC = CM

Area ( = * OA * RS

* RC * OS = * 16 * 24

RC = 192

RM = 2 * 192

= 384 m

So, distance between Ishita and Nisha is 384 m.