Question

A pole has to be erected at a point on the boundary of a circular ground of diameter 20 m in such a way that the difference of its distances from two diametrically opposite fixed gates P and Q on the boundary is 4 m. Is it possible to do so? If answer is yes at what distance from the two gates should the pole be erected?

Answer 1

Let “R” be the required location of the pole

Let the distance from the gate P is “x” m : PR = “x” m

The distance from the gate Q is (x + 4)m

∴ QR = (x + 4)m

In the right ∆PQR,

PR² + QR² = PQ² (By Pythagoras theorem)

x² + (x + 4)² = 20²

x² + x² + 16 + 8x = 400

2x² + 8x – 384 = 0

x² + 4x – 192 = 0  ...(divided by 2)

(x + 16) (x – 12) = 0

x + 16 = 0 or x – 12 = 0 ...[negative value is not considered]

x = – 16 or x = 12

Yes it is possible to erect

The distance from the two gates are 12 m and 16 m