Question

Example 17 : A pole has to be erected at a point on the boundary of a circular park
of diameter 13 metres in such a way that the differences of its distances from two
diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to
do so? If yes, at what distances from the two gates should the pole be erected?​

Answer 1

Answer:

OR OA= 5 m

then OB=5+7=12 m

Thus the pole is to be erected at 5m and 12 m fom the gates A and B.

Step-by-step explanation:

In the fig A and B are gates such that AB is a dia of the park

P is the given pole

∠APB=90° ( angle in a semicicle )

Let PA= x meter

then PB= x+7 m

In the ΔPAB using Pythagoras theorem

AB²=PA²+PB²

13²=x²+(x+7)²

169=x²+x²+14x+49

2x²+14x-120=0

Or x²+7x-60=0

x²+12x-5x-60=0

x(x+12)-5(x+12)=0

(x+12)(x-5)=0

x=-12 or 5

Length is not negative

So x=5

OR OA= 5 m

then OB=5+7=12 m

Thus the pole is to be erected at 5m and 12 m