Question

A pole has to be erected at a point on the boundary of a circular park of diameter 1 metres in such a way that the difference of its distance from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it the possible to do so? yes, at what distance from the two gates should the pole be erected?

Answer 1

At a distance of 5 meters from gate B.

Hint :

Let P be the required location of the pole such that its distance from gate B is x metres. i.e. BP = x metres.

$\therefore$ AP = x + 7

In right triangle APB, we have

$A{P}^2+P{B}^2=A{B}^2$

$\Rightarrow (x+7{)}^2+x^2={13}^2$

$\Rightarrow 2x^2+14x-120=0\Rightarrow x^2+7x-60=0\Rightarrow (x+12)(x-5)=0\Rightarrow x=5$