Question

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 distance from two diametrically opposite fixed gates A and B on the boundary is 7 m. At what distances from the two gates should the pole be erected? *
A. 3
B. 5
C. 12
D. None of these​

Answer 1

Step-by-step explanation:

The given situation is shown in the attached figure.

Given:

Diameter, AB=17 m

AC−BC=7

Solution:

From property of circles, ∠ACB=90

o

Using Pythagoras theorem,

AC

2

+BC

2

=AB

2

............(i)

AC−BC=7.............(ii)

Substituting AC from (ii) in (i), we get

(7+BC)

2

+BC

2

=17

2

BC

2

+7BC−120=0

BC

2

−8BC+15BC−120=0

(BC−8)(BC+15)=0

BC=−15,8

BC is a distance and cannot be negative

BC=8 m

AC=7+BC=15 m

Hence, it is possible to do so and the distance of the gates from the poles are 8 m and 15 m.

solution