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)

In ΔPAB,

AB^{2} = AP^{2} + BP^{2}

As *b* cannot be negative, so *b* = 5

∴ *a* = 7 + 5 = 12

Hence, PA = 12m and PB = 5m

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