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

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

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A pole has to be erected at a point on the boundary of a circular park...

Let P be the position of the pole and A and B be the opposite fixed gates.

PA - PB = 7 m

⇒ a - b = 7

⇒ a = 7 + b ..(1)

In Δ PAB,

AB^2 = AP^2 + BP^2

⇒ (17) = (a)^2 + (b)^2

⇒ a^2 + b^2 = 289

⇒ Putting the value of a = 7 + b in the above,

⇒ (7 + b)^2 + b^2 = 289

⇒ 49 + 14b + 2b^2 = 289

⇒ 2b^2 + 14b + 49 - 289 = 0

⇒ 2b^2 + 14b - 240 = 0

Dividing the above by 2, we get.

⇒ b^2 + 7b - 120 = 0

⇒ b^2 + 15b - 8b - 120 = 0

⇒ b(b + 15) - 8(b + 15) = 0

⇒ (b - 8) (b + 15) = 0

⇒ b = 8 or b = -15

Since this value cannot be negative, so b = 8 is the correct value.

Putting b = 8 in (1), we get.

a = 7 + 8

a = 15 m

Hence PA = 15 m and PB = 8 m

So, the distance from the gate A to pole is 15 m and from gate B to the pole is 8 m

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A pole has to be erected at a point on the boundary of a circular park of diameter 17 m in such a way that the difference of its distances from two diametrically opposite fixed gate A and B on the boundary is 7 m .Is it possible to do so ?If yes , at what distance from the two gates should the pole be erected? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A pole has to be erected at a point on the boundary of a circular park of diameter 17 m in such a way that the difference of its distances from two diametrically opposite fixed gate A and B on the boundary is 7 m .Is it possible to do so ?If yes , at what distance from the two gates should the pole be erected? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pole has to be erected at a point on the boundary of a circular park of diameter 17 m in such a way that the difference of its distances from two diametrically opposite fixed gate A and B on the boundary is 7 m .Is it possible to do so ?If yes , at what distance from the two gates should the pole be erected?.

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