Asked in: July 2024 board paperThe diameter of circular garden is 13 metre. The distance between two gates of garden is 13 metre. An electric pole is to be erected on the circumference of the garden such that the difference between distance of the po…

Answer: Yes. The pole is 5 m from one gate and 12 m from the other.

[Figure: circular garden with gates A and B at the ends of a diameter AB = 13 m; pole P on the circle; PA and PB joined.]

The distance between the gates equals the diameter, so the gates A and B are at the ends of a diameter.

P is on the circle, so \(\angle APB = 90^\circ\) (angle inscribed in a semicircle).

Let PA = x m; then PB = (x + 7) m. By Pythagoras theorem, \(x^2 + (x + 7)^2 = 13^2\).

\(2x^2 + 14x + 49 = 169\) \(\therefore x^2 + 7x - 60 = 0\) \(\therefore (x + 12)(x - 5) = 0\).

Distance cannot be negative, so x = 5. The pole can be erected: it is 5 m from one gate and 12 m from the other (check: \(25 + 144 = 169\)).