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  • A pole has to be erected at a point on the boundary of a circular park of diameter 13 m in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 m. Is it possible to do so? If yes, at w

A pole has to be erected at a point on the boundary of a circular park of diameter 13 m in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 m. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

 

 

Answers (1)

PB - PA = 7m

Let AP be x m.

So, PB = (x + 7) m

       \mathrm{AB^2 = PB^2 + AB^2}

       \mathrm{13^2 = (x +7)^2 + x^2}

       \mathrm{x^2 + 7x -60 = 0}

\mathrm{\Rightarrow (x+12)(x-5) = 0}

So,  x = 5 and x = -12 (not possible)

The distance of pole from the gate A = 5 m

The distance of pole from the gate B = 12 m

Posted by

Safeer PP

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