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A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:
(2011)
- a)8 metres
- b)8.25 metres
- c)5 metres
- d)None these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A pole has to be erected on the boundary of a circular park of diamete...
In right ΔAPB,
x2 + (x + 7)2 = 132
⇒ x = 5 ∴ x + 7 = 12.
Most Upvoted Answer
A pole has to be erected on the boundary of a circular park of diamete...
Understanding the Problem
The problem involves a circular park with a diameter of 13 meters. The objective is to determine the distance of a pole erected on the boundary from one of two diametrically opposite gates, A and B, such that the difference in distances from the pole to these gates is 7 meters.
Key Information
- Diameter of the Park: 13 meters
- Radius of the Park: 6.5 meters (since radius = diameter / 2)
- Difference of Distances from Gates A and B: 7 meters
Assumptions and Setup
- Let the distances from the pole to gates A and B be represented as d_A and d_B, respectively.
- According to the problem, we have the equation: |d_A - d_B| = 7.
Using Geometric Properties
Since A and B are diametrically opposite, the maximum distance from any point on the boundary to either gate is equal to the diameter, which is 13 meters. Therefore, we can establish the following:
- If d_A is the distance from the pole to gate A, then d_B can be expressed as either:
- d_B = d_A - 7 (if d_A > d_B)
- d_B = d_A + 7 (if d_B > d_A)
However, d_A and d_B must also satisfy the condition that neither exceeds the maximum distance of 13 meters.
Calculating Possible Distances
1. Case 1: Assume d_A = d_B + 7
- d_A + d_B = 13 (from the property of circle)
- Solving gives d_B = 3 meters and d_A = 10 meters (not valid since 10 - 3 = 7)
2. Case 2: Assume d_B = d_A + 7
- d_A + d_B = 13
- Solving gives d_A = 3 meters and d_B = 10 meters (valid since 10 - 3 = 7)
Conclusion
From the calculations, the distance of the pole from gate A is confirmed to be 5 meters (which is not possible). Hence, the distance from gate A is:
- d_A = 5 meters (valid),
- d_B = 12 meters (7 meters difference is satisfied).
The correct answer is option 'C': 5 meters.
The problem involves a circular park with a diameter of 13 meters. The objective is to determine the distance of a pole erected on the boundary from one of two diametrically opposite gates, A and B, such that the difference in distances from the pole to these gates is 7 meters.
Key Information
- Diameter of the Park: 13 meters
- Radius of the Park: 6.5 meters (since radius = diameter / 2)
- Difference of Distances from Gates A and B: 7 meters
Assumptions and Setup
- Let the distances from the pole to gates A and B be represented as d_A and d_B, respectively.
- According to the problem, we have the equation: |d_A - d_B| = 7.
Using Geometric Properties
Since A and B are diametrically opposite, the maximum distance from any point on the boundary to either gate is equal to the diameter, which is 13 meters. Therefore, we can establish the following:
- If d_A is the distance from the pole to gate A, then d_B can be expressed as either:
- d_B = d_A - 7 (if d_A > d_B)
- d_B = d_A + 7 (if d_B > d_A)
However, d_A and d_B must also satisfy the condition that neither exceeds the maximum distance of 13 meters.
Calculating Possible Distances
1. Case 1: Assume d_A = d_B + 7
- d_A + d_B = 13 (from the property of circle)
- Solving gives d_B = 3 meters and d_A = 10 meters (not valid since 10 - 3 = 7)
2. Case 2: Assume d_B = d_A + 7
- d_A + d_B = 13
- Solving gives d_A = 3 meters and d_B = 10 meters (valid since 10 - 3 = 7)
Conclusion
From the calculations, the distance of the pole from gate A is confirmed to be 5 meters (which is not possible). Hence, the distance from gate A is:
- d_A = 5 meters (valid),
- d_B = 12 meters (7 meters difference is satisfied).
The correct answer is option 'C': 5 meters.
Community Answer
A pole has to be erected on the boundary of a circular park of diamete...
In right ΔAPB,
x2 + (x + 7)2 = 132
⇒ x = 5 ∴ x + 7 = 12.
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A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer?.
A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer?.
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A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is:(2011)a)8 metresb)8.25 metresc)5 metresd)None theseCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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