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Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle is
- a)1/3
- b)2/5
- c)3/5
- d)1/5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three circles A, B and C have a common center O. A is the inner circle...
let ox=1
ar. of A: (pie)
ar. of B: 4(pie)
ar. of C: 9(pie)
subtract to get middle areas
ratio = 3/5
Most Upvoted Answer
Three circles A, B and C have a common center O. A is the inner circle...
Let's consider the radius of the inner circle A as r, the radius of the middle circle B as 2r, and the radius of the outer circle C as 3r.
1. Calculate the areas of the three circles:
- The area of circle A is πr^2.
- The area of circle B is π(2r)^2 = 4πr^2.
- The area of circle C is π(3r)^2 = 9πr^2.
2. Calculate the areas of the regions between the circles:
- The area between circles A and B is the difference between the area of circle B and the area of circle A: 4πr^2 - πr^2 = 3πr^2.
- The area between circles B and C is the difference between the area of circle C and the area of circle B: 9πr^2 - 4πr^2 = 5πr^2.
3. Calculate the areas of the regions defined by the tangents:
- The area of the triangle OXP is (1/2)(OX)(XP) = (1/2)(r)(r) = (1/2)r^2.
- The area of the triangle OYP is (1/2)(OY)(YP) = (1/2)(2r)(r) = r^2.
- The area of the triangle PXY is (1/2)(XY)(PY) = (1/2)(r)(r) = (1/2)r^2.
4. Calculate the ratio of the area between the inner and middle circles to the area between the middle and outer circle:
- The area between the inner and middle circles is 3πr^2.
- The area between the middle and outer circles is 5πr^2.
- The ratio of these two areas is (3πr^2)/(5πr^2) = 3/5.
Therefore, the correct answer is option 'C': 3/5.
1. Calculate the areas of the three circles:
- The area of circle A is πr^2.
- The area of circle B is π(2r)^2 = 4πr^2.
- The area of circle C is π(3r)^2 = 9πr^2.
2. Calculate the areas of the regions between the circles:
- The area between circles A and B is the difference between the area of circle B and the area of circle A: 4πr^2 - πr^2 = 3πr^2.
- The area between circles B and C is the difference between the area of circle C and the area of circle B: 9πr^2 - 4πr^2 = 5πr^2.
3. Calculate the areas of the regions defined by the tangents:
- The area of the triangle OXP is (1/2)(OX)(XP) = (1/2)(r)(r) = (1/2)r^2.
- The area of the triangle OYP is (1/2)(OY)(YP) = (1/2)(2r)(r) = r^2.
- The area of the triangle PXY is (1/2)(XY)(PY) = (1/2)(r)(r) = (1/2)r^2.
4. Calculate the ratio of the area between the inner and middle circles to the area between the middle and outer circle:
- The area between the inner and middle circles is 3πr^2.
- The area between the middle and outer circles is 5πr^2.
- The ratio of these two areas is (3πr^2)/(5πr^2) = 3/5.
Therefore, the correct answer is option 'C': 3/5.
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Community Answer
Three circles A, B and C have a common center O. A is the inner circle...
let the radius of the A circle be x..
so.. radii of B and C are 2x and 3x respectively.
Area of the first given part will be pi(2x)^2 - pi(x)^2 = 3pi x^2 ---1
Area of the second given part will be pi(3x)^2 - pi(2x)^2 = 5pi x^2 ---2
dividing 1 and 2... we get 3/5
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Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer?
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Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. 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 Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer?.
Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. 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 Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer?.
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Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Three circles A, B and C have a common center O. A is the inner circle, B middle circle and C is outer circle. The radius of the outer circle C, OP cuts the inner circle at X and middle circle at Y such that OX = XY = YP. The ratio of the area of the region between the inner and middle circles to the area of the region between the middle and outer circle isa)1/3b)2/5c)3/5d)1/5Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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