Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius 20 m drawn in a park.

Solution:

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

AR = AS = 24/2 = 12 cm

OR = OS = OM = 20 cm   [Radii of circle]

In ΔOAR,

$O A^{2}+A R^{2}=O R^{2}$

$\mathrm{OA}^{2}+12^{2}=20^{2}$

$O A^{2}=400-144=256 \mathrm{~m}^{2}$

OA = 16 m

We know that, in an isosceles triangle altitude divides the base.

So in ΔRSM, ∠RCS = 90° and RC = CM

Area of ΔORS = 1/2 × OA × RS

⇒ 1/2 × RC × OS = 1/2 × 16 × 24

⇒ RC × 20 = 16 × 24

⇒ RC = 19.2

⇒ RM = 2(19.2) = 38.4 m

So, the distance between Ishita and Nisha is 38.4 m.