Let the positions ofReshma, Salma and Mandip be represented as A, B and C respectively.
From the question, weknow that AB = BC = 6cm.
So, the radius of thecircle i.e. OA = 5cm
Now, draw aperpendicular BM тКе AC.
Since AB = BC, ABC canbe considered as an isosceles triangle. M is mid-point of AC. BM is theperpendicular bisector of AC and thus it passes through the centre of thecircle.
Now,
let AM = y and
OM = x
So, BM will be =(5-x).
By applying Pythagoreantheorem in ╬ФOAM we get,
OA2┬а=OM2┬а+AM2
тЗТ 52┬а=x2┬а+y2┬атАФ (i)
Again, by applyingPythagorean theorem in ╬ФAMB,
AB2┬а=BM2┬а+AM2
тЗТ 62┬а=(5-x)2+y2┬атАФ (ii)
Subtracting equation(i) from equation (ii), we get
36-25 = (5-x)2┬а+y2┬а-x2-y2
Now, solving thisequation we get the value of x as
x = 7/5
Substituting the valueof x in equation (i), we get
y2┬а+(49/25)= 25
тЗТ y2┬а=25 тАУ (49/25)
Solving it we get thevalue of y as
y = 24/5
Thus,
AC = 2├ЧAM
= 2├Чy
= 2├Ч(24/5) m
AC = 9.6 m
So, the distancebetween Reshma and Mandip is 9.6 m.