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} + x^{2}
⇒ x^{2} +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.