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 and 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.​

Answer 1

$\huge\underline\mathbb{SOLUTION:-}$

$\mathsf {AB = 13\:m}$

$\mathsf {BP = x}$

$\implies \mathsf {AP - BP = 7}$

$\implies \mathsf {AP = x + 7}$

$\underline \mathsf{ATQ:-}$

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

$\implies \mathsf {x^2 + 7x - 60 = 0}$

$\mathsf {(x + 12)\:(x - 5) = 0}$

$\implies \mathsf {x = -12\: N.P}$

$\mathsf \blue{x = 5}$

$\therefore \mathsf {Pole\:has\:to\:be\:erected\:at\:a\:distance\:of\:5\:m}$

$\mathsf {\: \: \: \:from\:gate\:B\:and\:12\:m\:from\:gate\:A.}$