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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?`
one year ago

```							Let  O bethe centre of the circle. A, B and C represent the positions of Reshma, Salmaand Mandip. AB = 6cm and BC = 6cm.Radius OA = 5cm. (given) Draw BM ⊥ AC ABC is an isosceles triangle as AB = BC, M ismid-point of AC. BM isperpendicular bisector of AC and thus it passes through the centre of thecircle. Let AM = y and OM = x then BM = (5-x).  In ΔOAM,OA²=OM²+AM² ( by Pythagorastheorem) 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) - x²11= 25+x²-10x - x²11= 25-10x10x = 14  x= 7/5 Substituting the value of x in (i), we get y²+ 49/25 = 25y² =25 – 49/25y² =(625 – 49)/25y²=576/25 y = 24/5 Thus,AC = 2×AMAC = 2×y AC= 2×(24/5) m = 48/5 m = 9.6 mHence, the Distance between Reshma and Mandipis 9.6 m.
```
one year ago
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