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

Answer 1

AB = 13 m
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
 Therefore,Pole has to be erected at a distance of 5m from gate B & 12m from gate A.