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

Thus, it is possible to erect a pole at a point p on the boundary of the park at distances 5m and 12m respectively from gates B and A.

Step-by-step explanation:

Let P be the required location of pole .

A and B are the two gates.

Let the distance of pole at p from gate be 'x' meters

i.e. PB = x m

•°• AP = (x + 7)m and AB = 13 m

•°• AP² + BP² = AB² => (x +7)² + x =13²

Rejecting x =-12, we get x = 5

•°• PB = 5m

and

AP = 12m

(I hope this helped :)