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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 le...
B In figure AE*BE=CE*DE (The intersecting chords 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 le...
B In figure AE*BE=CE*DE (The intersecting chords 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
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Community Answer
In a circle of radius 11 cm, CD is a diameter and AB is a chord of le...
Given:
- Radius of the circle = 11 cm
- CD is a diameter, so its length = 2 * radius = 2 * 11 cm = 22 cm
- AB is a chord of length 20.5 cm
- CE has length 7 cm
To find: The difference of the lengths of BE and AE
Solution:
1. Drawing the diagram:
- Let O be the center of the circle.
- Draw the circle with radius 11 cm and mark the center as O.
- Draw the diameter CD perpendicular to AB.
- Mark the point of intersection of AB and CD as E.
- Draw the radius OE and mark the length as x.
- Draw the radius OB and mark the length as y.
- Draw the radius OA and mark the length as z.
2. Analyzing the diagram:
- Since CD is a diameter, CE is perpendicular to AD and EB is perpendicular to AD.
- In right triangle OCE, using Pythagoras theorem, we have: (OC)^2 = (OE)^2 + (CE)^2
- In right triangle OBE, using Pythagoras theorem, we have: (OB)^2 = (OE)^2 + (BE)^2
- In right triangle OAE, using Pythagoras theorem, we have: (OA)^2 = (OE)^2 + (AE)^2
3. Expressing the lengths in terms of x, y, and z:
- From the above analysis, we can write the following equations:
- (11)^2 = x^2 + (7)^2
- (11)^2 = x^2 + (y-20.5)^2
- (11)^2 = x^2 + (z-20.5)^2
4. Solving the equations:
- From the first equation, we get: x^2 = (11)^2 - (7)^2 = 121 - 49 = 72
- Substituting this value of x^2 in the second equation, we get: (11)^2 = 72 + (y-20.5)^2
- Simplifying, we get: (y-20.5)^2 = (11)^2 - 72 = 121 - 72 = 49
- Taking the square root on both sides, we get: y-20.5 = 7 or y-20.5 = -7
- Solving these equations, we get: y = 27.5 or y = 13.5
- Substituting this value of x^2 in the third equation, we get: (11)^2 = 72 + (z-20.5)^2
- Simplifying, we get: (z-20.5)^2 = (11)^2 - 72 = 121 - 72 = 49
- Taking the square root on both sides, we get: z-20.5 = 7 or z-20.5 = -7
- Solving these equations, we get: z = 27.5 or z = 13.5
5. Calculating the lengths of BE and AE:
- Since AB is a chord, we know that AE = EB.
- So, the difference of the lengths of BE and AE = BE - AE = y - z
- Radius of the circle = 11 cm
- CD is a diameter, so its length = 2 * radius = 2 * 11 cm = 22 cm
- AB is a chord of length 20.5 cm
- CE has length 7 cm
To find: The difference of the lengths of BE and AE
Solution:
1. Drawing the diagram:
- Let O be the center of the circle.
- Draw the circle with radius 11 cm and mark the center as O.
- Draw the diameter CD perpendicular to AB.
- Mark the point of intersection of AB and CD as E.
- Draw the radius OE and mark the length as x.
- Draw the radius OB and mark the length as y.
- Draw the radius OA and mark the length as z.
2. Analyzing the diagram:
- Since CD is a diameter, CE is perpendicular to AD and EB is perpendicular to AD.
- In right triangle OCE, using Pythagoras theorem, we have: (OC)^2 = (OE)^2 + (CE)^2
- In right triangle OBE, using Pythagoras theorem, we have: (OB)^2 = (OE)^2 + (BE)^2
- In right triangle OAE, using Pythagoras theorem, we have: (OA)^2 = (OE)^2 + (AE)^2
3. Expressing the lengths in terms of x, y, and z:
- From the above analysis, we can write the following equations:
- (11)^2 = x^2 + (7)^2
- (11)^2 = x^2 + (y-20.5)^2
- (11)^2 = x^2 + (z-20.5)^2
4. Solving the equations:
- From the first equation, we get: x^2 = (11)^2 - (7)^2 = 121 - 49 = 72
- Substituting this value of x^2 in the second equation, we get: (11)^2 = 72 + (y-20.5)^2
- Simplifying, we get: (y-20.5)^2 = (11)^2 - 72 = 121 - 72 = 49
- Taking the square root on both sides, we get: y-20.5 = 7 or y-20.5 = -7
- Solving these equations, we get: y = 27.5 or y = 13.5
- Substituting this value of x^2 in the third equation, we get: (11)^2 = 72 + (z-20.5)^2
- Simplifying, we get: (z-20.5)^2 = (11)^2 - 72 = 121 - 72 = 49
- Taking the square root on both sides, we get: z-20.5 = 7 or z-20.5 = -7
- Solving these equations, we get: z = 27.5 or z = 13.5
5. Calculating the lengths of BE and AE:
- Since AB is a chord, we know that AE = EB.
- So, the difference of the lengths of BE and AE = BE - AE = y - z
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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?
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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? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC 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 SSC 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 SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC 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 SSC 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?.
Solutions 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 English & in Hindi are available as part of our courses for SSC.
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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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