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Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest to
- a)7.2
- b)7.8
- c)6.6
- d)8.8
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let C be a circle of radius 5 meters having center at O. Let PQ be a c...
OT = 2.4M
In ΔOTQ
OQ2 = OT2 + TQ2 ⇒ TQ2 = OQ2 - OT2
= (5)2 - (2.4)2
=19.24
Most Upvoted Answer
Let C be a circle of radius 5 meters having center at O. Let PQ be a c...
Given:
- Circle C has a radius of 5 meters and its center is at point O.
- Chord PQ passes through points A and B.
- Point A is located 4 meters north of O.
- Point B is located 3 meters east of O.
To find:
The length of chord PQ.
Solution:
Step 1: Calculate the length of AO and BO
Using Pythagoras theorem, we can find the length of AO and BO.
Length of AO = √(radius^2 - distance^2) = √(5^2 - 4^2) = √(25 - 16) = √9 = 3 meters
Length of BO = √(radius^2 - distance^2) = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 meters
Step 2: Calculate the length of AB
Using the distance formula, we can find the length of AB.
Length of AB = √((x2 - x1)^2 + (y2 - y1)^2) = √((3 - 0)^2 + (4 - 0)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 meters
Step 3: Calculate the length of PQ
Since PQ is a chord passing through the center of the circle, it bisects AB.
Length of PQ = (Length of AB)/2 = 5/2 = 2.5 meters
However, we are looking for the nearest whole number, so we round up to the nearest whole number.
Length of PQ (rounded up) = 3 meters
Conclusion:
The length of chord PQ is nearest to 3 meters. Therefore, the correct option is D.
- Circle C has a radius of 5 meters and its center is at point O.
- Chord PQ passes through points A and B.
- Point A is located 4 meters north of O.
- Point B is located 3 meters east of O.
To find:
The length of chord PQ.
Solution:
Step 1: Calculate the length of AO and BO
Using Pythagoras theorem, we can find the length of AO and BO.
Length of AO = √(radius^2 - distance^2) = √(5^2 - 4^2) = √(25 - 16) = √9 = 3 meters
Length of BO = √(radius^2 - distance^2) = √(5^2 - 3^2) = √(25 - 9) = √16 = 4 meters
Step 2: Calculate the length of AB
Using the distance formula, we can find the length of AB.
Length of AB = √((x2 - x1)^2 + (y2 - y1)^2) = √((3 - 0)^2 + (4 - 0)^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 meters
Step 3: Calculate the length of PQ
Since PQ is a chord passing through the center of the circle, it bisects AB.
Length of PQ = (Length of AB)/2 = 5/2 = 2.5 meters
However, we are looking for the nearest whole number, so we round up to the nearest whole number.
Length of PQ (rounded up) = 3 meters
Conclusion:
The length of chord PQ is nearest to 3 meters. Therefore, the correct option is D.
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Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer?
Question Description
Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer?.
Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatpasses through points A and B where A is located 4 meters north of O and B is located 3meters east of O. Then, the length of PQ, in meters, is nearest toa)7.2b)7.8c)6.6d)8.8Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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