Question

Three girls Reshma, salma and Mandip are playing a game by standing on a circle of radius $5m$ drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and berween Salma and Mandip is $6m$ each, what is the distance between Reshma and Mandip?

Answer 1

We know $R=\frac{arc}{4\Delta }$

Let distance between reshma and mandip is ${}^{\prime }{a}^{\prime }$ is

$\therefore 5=\frac{36a}{4\sqrt{(6+\frac{a}{2})\left(\frac{a}{2}\right)(6-\frac{a}{2})}}5=\frac{9a}{\frac{a}{2}\sqrt{36-\frac{a^2}{4}}}\Rightarrow 5=\frac{18}{\sqrt{36-\frac{a^2}{4}}}\Rightarrow 36-\frac{a^2}{4}=\frac{{18}^2}{25}\Rightarrow \frac{a^2}{4}=36-\frac{{18}^2}{25}\Rightarrow a^2=\frac{36\times 25-{18}^2}{25}\times 4\Rightarrow a^2=\frac{36\times 16\times 4}{25}\Rightarrow a=\frac{6\times 4\times 2}{5}=\frac{48}{5}=9.6m$