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

Let P be the position of the pole and A and B be the opposite fixed gates.

PA – PB = 7

a – b = 7

a = 7 + b  ...(1)


AB2 = AP2 + BP2

As b cannot be negative, so b = 5

a = 7 + 5 = 12

Hence, PA = 12m and PB = 5m

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