Question

3 girls sapna, mariam and naveena are playing a game by standing on a circle of radius 5m drawn in a park. sapna throws a ball to mariam, m arium to naveena, naveena to sapna. if the distance between sapna and mariam and between marium and naveena is 6m each, what is the distance between spna and naveena.

Answer 1

FIGURE IS IN THE ATTACHMENT
Let O be the centre of the circle. A, B and C represent the positions of Sapna, Mariam and Naveena.
AB = 6cm and BC = 6cm.
Radius OA = 5cm. (given)
Draw BM ⊥ AC
ABC is an isosceles triangle as AB = BC, M is mid-point of AC.
BM is perpendicular bisector of AC and thus it passes through the centre of the circle.
Let AM = y and OM = x then BM = (5-x).
In ΔOAM,
OA²=OM²+AM² ( by Pythagoras theorem)
5²=x²+ y²— (i)
In ΔAMB,
AB²=BM² +AM² (by Pythagoras theorem)
6²= (5-x)²+y² — (ii)
Subtracting (i) from (ii),
36 – 25 = (5-x)² -x²
11 = (25+ x²– 2×5×x) - x²
11= 25+x²-10x - x²
11= 25-10x
10x = 14
x= 7/5
Substituting the value of x in (i), we get
y²+ 49/25 = 25
y² = 25 – 49/25
y² = (625 – 49)/25
y²= 576/25
y = 24/5
Thus,
AC = 2×AM
AC = 2×y
AC= 2×(24/5) m
= 48/5 m = 9.6 m
Hence, the Distance between Sapna and Naveena is 9.6 m

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