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In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
- a)2.5
- b)1.5
- c)3.5
- d)0.5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a circle of radius 11 cm, CD is a diameter and AB is a chord of len...
In figure AE*BE=CE*DE (Ptolemy Theorem)
=> 7*15= x(20.5-x) (Assuming AE=x)
=> 210=x(41-2x)
=> 2x2-41x+210=0
=> x=10 or x=10.5 => AE=10 or AE=10.5 Hence BE = 20.5-10=10.5 or BE = 20.5-10.5=10
Required difference= 10.5-10=0.5
Most Upvoted Answer
In a circle of radius 11 cm, CD is a diameter and AB is a chord of len...
Given:
- A circle of radius 11 cm with diameter CD
- AB is a chord of length 20.5 cm
- AB and CD intersect at E inside the circle
- CE has length 7 cm
To Find: The difference of the lengths of BE and AE
Solution:
1. Draw the circle and label the given points and lengths.
2. Using the intersecting chord theorem, we know that:
AE × EB = CE × ED
Substituting the given values, we get:
AE × EB = 7 × 14
AE × EB = 98
3. We also know that:
AE + EB = AB
Substituting the given value, we get:
AE + EB = 20.5
4. We can use algebra to solve for AE and EB. Rearranging the equation in step 3, we get:
EB = 20.5 - AE
Substituting this in the equation from step 2, we get:
AE × (20.5 - AE) = 98
Expanding the brackets and rearranging, we get a quadratic equation:
AE² - 20.5AE + 98 = 0
5. Solving this quadratic equation using the quadratic formula, we get:
AE = 10.25 ± 3.75
AE = 14 or AE = 6.5
6. We can discard the solution AE = 14 since it would make EB negative, which is not possible. Therefore, AE = 6.5 and EB = 14 - 6.5 = 7.5.
7. Finally, the difference between BE and AE is:
BE - AE = 7.5 - 6.5 = 1
Therefore, the correct answer is option D (0.5 is not a valid option).
- A circle of radius 11 cm with diameter CD
- AB is a chord of length 20.5 cm
- AB and CD intersect at E inside the circle
- CE has length 7 cm
To Find: The difference of the lengths of BE and AE
Solution:
1. Draw the circle and label the given points and lengths.
2. Using the intersecting chord theorem, we know that:
AE × EB = CE × ED
Substituting the given values, we get:
AE × EB = 7 × 14
AE × EB = 98
3. We also know that:
AE + EB = AB
Substituting the given value, we get:
AE + EB = 20.5
4. We can use algebra to solve for AE and EB. Rearranging the equation in step 3, we get:
EB = 20.5 - AE
Substituting this in the equation from step 2, we get:
AE × (20.5 - AE) = 98
Expanding the brackets and rearranging, we get a quadratic equation:
AE² - 20.5AE + 98 = 0
5. Solving this quadratic equation using the quadratic formula, we get:
AE = 10.25 ± 3.75
AE = 14 or AE = 6.5
6. We can discard the solution AE = 14 since it would make EB negative, which is not possible. Therefore, AE = 6.5 and EB = 14 - 6.5 = 7.5.
7. Finally, the difference between BE and AE is:
BE - AE = 7.5 - 6.5 = 1
Therefore, the correct answer is option D (0.5 is not a valid option).
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In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer?
Question Description
In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct 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 In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct 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 In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer?.
In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct 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 In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct 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 In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer?.
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In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, isa)2.5b)1.5c)3.5d)0.5Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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