Three girls Reshma, Salma, and Mandip are playing a game standing on a circle of radius 5 metres drawn in a park. Reshma throws a ball to Salma, Salma to Mandip; Mandip to Reshma. The distance between Reshma and Salma and between Salma And Mandeep is 6 metre each. What is the distance between Reshma and Mandip?
Given:
Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius \( 5 \mathrm{~m} \) drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. The distance between Reshma and Salma and between Salma and Mandip is \( 6 \mathrm{~m} \) each.
To do:
We have to find the distance between Reshma and Mandip.
Solution:
Let $R, S$ and $M$ be the positions of Reshma, Salma, and Mandip respectively. Draw perpendicular $OA$ and $OB$ on $RS$ and $SM$ respectively.
$AR=AS= \frac{6}{2} =3\ m$
$OR=OS=OM=5\ m$ [Radii of the circle]
In $\triangle OAR$
$OA^2 + AR^2 = OR^2$
$OA^2 + 3^2 = 5^2$
$OA^2= 25−9$
$OA^2=16$
$OA=4\ m$
We know that,
In an isosceles triangle, altitude divides the base.
So, in $\triangle RSM$
$\angle RCS=90^o$
$RC=CM$
Area of $\triangle ORS= \frac{1}{2} \times OA \times RS$
$\frac{1}{2} \times RC \times OS= \frac{1}{2}\times4\times6$
$RC\times 5=24$
$RC=4.8\ m$
$RM=2RC=2\times4.8=9.6\ m$
So, the distance between Reshma and Mandip is $9.6\ m$.
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