Question

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

Answer 1

PQ = 20 m

PX – XQ = 4 m … (1)

Squaring both sides,

PX² + XQ² – 2PX . QX = 16 (∵ ∠Q x p = 90°)

PQ² – 2P x QX = 16

400 – 16 = 2PX x QX

384 = 2PX – QX

PX . QX = 192

∴ (PX + QX) = PX + QX + 2PX . QX

= 400 + 2 x 192

= 784 = 28²

∴ PX + QX = 28

From (1) & (2) 2PX = 32 ⇒ PX = 16 m QX = 12 m

∴Yes, the distance from the two gates to the pole PX and QX is 12 m, 16m.