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 between Salma and Mandip

Explanation

Let three girls Reshma, Salma and Mandip be at R,S and M.
`therefore RS=SM=6M`. (Given)
Now, `angleROS =angle SOM` (equal chords of a circle subtend equal angles at the centre)
`rArrangle RON=angleMON`
In `Delta ONR` and `DeltaONM`, we have
`because" "{(OR,=,,OM,("each radii")),(angleRON,=,,angleMON,("just proved")),(ON,=,,ON,("common")):}`
`thereforeDeltaONRcongDeltaONM` (SAS congruency)
`therefore` RN=NM(c.p.c.t) ......(1)
and `angleRNO=angle MNO` (c.p.c.t)
But `angle RNO+angleMNO=180^@` (L.P.A)
`thereforeangleRNO=angleMNO=90^@`
`rArrONbotRM`
Let `ON=xm`.
`therefore NS =(5-x)m`
Now, in right `Delta ONR` ,
`RN^2=OR^2-ON^2` (by Pythagoras theorem) ......(1)
`rArrRN^2=25-x^2`
right `Delta RNS`,
`RN^2=RS^2-NS^2` (by Pythagoras theorem)......(2)
`rArrRN^2=36-(5-x)^2`
From eqs. (1) and (2),we get
`25-x^2=36-(5-x)^2`