Question

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

• A. 9 m
• B. 9.6 m
• C. 10 m
• D. 10.6 m

Answer 1

The correct option is B $9.6m$

Given: $RS=SM=6m$

Radius $=OR=OS=5m$

In Right angled triangle $\Delta RCO$

${RC}^2={OR}^2-{OC}^2..........\left(1\right)$

In Right angled triangle $\Delta SCR$

${RC}^2={RS}^2-{SC}^2...............\left(2\right)$

From $eq.\left(1\right)$ and $\left(2\right),$ we get

${OR}^2-{OC}^2={RS}^2-{SC}^2$

$5^2-x^2=6^2-(5-x{)}^2$

(let $OC=x$)

$25-x^2=36-x^2-25+10x$

$\Rightarrow 10x=-36+25+25$

$\Rightarrow 10x=14$

$\Rightarrow x=\frac{14}{10}$

Distance between Reshma and Mandeep $=RM$

$=2RC=2\sqrt{{OR}^2-{OC}^2}$

$=2\sqrt{{25}^2-x^2}$

$=2\sqrt{25-{\left(\frac{14}{10}\right)}^2}$

$=2\sqrt{\left(\frac{2500-196}{100}\right)}$

$=2\sqrt{\left(\frac{2304}{10}\right)}$

$=2\times \sqrt{(\frac{48}{10}{)}^2}$

$=2\times \frac{48}{10}$

$=\frac{48}{5}=9.6m$