What distances from the two gates should the pole, Mathematics

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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 differences of its distances from two diametrically opposite fixed gates A & B on the boundary in 7m.  Is it possible to do so?  If answer is yes at what distances from the two gates should the pole be erected.

Ans:    AB = 13 m                                                                        P BP = x

⇒ AP - BP = 7

⇒  AP = x + 7

APQ

⇒ (13)2 = (x + 7)2 + x2

x2 +7x - 60 = 0

(x + 12) (x - 5) = 0

x = - 12 N.P

x = 5

∴Pole has to be erected at a distance of 5m from gate B & 12m from gate A.


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