Math, asked by ItzDazzingBoy, 2 months ago


 \huge\mathbb \purple{QUESTION}
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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Answers

Answered by Gorgeousqueen01
37

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.

Answered by vishalverma5690
3

your answer in attachment

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