A pole has to be erected at a point on the boundary of a circular park of a diameter 13 m in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on boundary is 7 meters . is it possible to do so? if yes , at what distances from the two gates should the poles be erected?
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Answer:
The given situation is shown in the attached figure.
Given:
Diameter, AB=17 m
AC−BC=7
Solution
From property of circles, ∠ACB=90°
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.
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