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The girl teams , 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. Distance between teams and Salma, Salma and Mandip is equal of 6m each what is the distance between teams and Salma?

The girl teams , 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. Distance between teams and Salma, Salma and Mandip is equal of 6m each what is the distance between teams and Salma?

Question Image
Grade:10

1 Answers

Arun
25763 Points
2 years ago
Let  O be
the centre of the circle. A, B and C represent the positions of Reshma, Salma
and Mandip.
 
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 Reshma and Mandip
is 9.6 m.
 

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