Question

a pole has to be erected at a point on the boundary of a circular Park of diameter 13m in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7m. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
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Answer 1

let one gate at distance= x
another one is =x+7
atq it formed right ane triangle
so we apply pythagoras,
x^2+(x+7)^2=13^2
2x^2+49+14x=169
x^2+7x-60=0
x^2+12x-5x-60=0
x=-12 and 5
so we take 5 bcz lenght cant be negative
so answer is 5 or 12