SSC CGL Exam > SSC CGL Questions > AB = 8 cm and CD = 6 cm are two parallel chor...
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AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle is
- a)5 cm
- b)4 cm
- c)3 cm
- d)2 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
AB = 8 cm and CD = 6 cm are two parallel chords on the same side of th...
Understanding the Problem
Given two parallel chords AB and CD of lengths 8 cm and 6 cm respectively, and the distance between them is 1 cm. We need to find the radius of the circle.
Visualizing the Setup
- Place the center of the circle at point O.
- Let the distance from O to chord AB be x cm.
- Thus, the distance from O to chord CD will be (x + 1) cm since they are 1 cm apart.
Using the Properties of Chords
1. Length of Chord AB:
- The distance from the center to the chord can be calculated using the formula:
r^2 = (AB/2)^2 + (distance to AB)^2
- For AB (8 cm):
r^2 = (4)^2 + x^2
r^2 = 16 + x^2
2. Length of Chord CD:
- Similarly, for CD (6 cm):
r^2 = (CD/2)^2 + (distance to CD)^2
- For CD (6 cm):
r^2 = (3)^2 + (x + 1)^2
r^2 = 9 + (x + 1)^2
r^2 = 9 + x^2 + 2x + 1
r^2 = 10 + x^2 + 2x
Setting the Equations Equal
- Since both expressions equal r^2, we can set them equal to each other:
16 + x^2 = 10 + x^2 + 2x
Simplifying the Equation
- Canceling x^2 from both sides:
16 = 10 + 2x
6 = 2x
x = 3 cm
Finding the Radius
- Substitute x back to find the radius:
r^2 = 16 + (3)^2
r^2 = 16 + 9
r^2 = 25
r = 5 cm
Conclusion
Therefore, the radius of the circle is 5 cm, which confirms option A is correct.
Given two parallel chords AB and CD of lengths 8 cm and 6 cm respectively, and the distance between them is 1 cm. We need to find the radius of the circle.
Visualizing the Setup
- Place the center of the circle at point O.
- Let the distance from O to chord AB be x cm.
- Thus, the distance from O to chord CD will be (x + 1) cm since they are 1 cm apart.
Using the Properties of Chords
1. Length of Chord AB:
- The distance from the center to the chord can be calculated using the formula:
r^2 = (AB/2)^2 + (distance to AB)^2
- For AB (8 cm):
r^2 = (4)^2 + x^2
r^2 = 16 + x^2
2. Length of Chord CD:
- Similarly, for CD (6 cm):
r^2 = (CD/2)^2 + (distance to CD)^2
- For CD (6 cm):
r^2 = (3)^2 + (x + 1)^2
r^2 = 9 + (x + 1)^2
r^2 = 9 + x^2 + 2x + 1
r^2 = 10 + x^2 + 2x
Setting the Equations Equal
- Since both expressions equal r^2, we can set them equal to each other:
16 + x^2 = 10 + x^2 + 2x
Simplifying the Equation
- Canceling x^2 from both sides:
16 = 10 + 2x
6 = 2x
x = 3 cm
Finding the Radius
- Substitute x back to find the radius:
r^2 = 16 + (3)^2
r^2 = 16 + 9
r^2 = 25
r = 5 cm
Conclusion
Therefore, the radius of the circle is 5 cm, which confirms option A is correct.
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Community Answer
AB = 8 cm and CD = 6 cm are two parallel chords on the same side of th...
On the basis of question we draw a figure of a circle with centre O ,
Let OE = y cm
then OF = (y +1) cm
OA = OC = r cm
AE = 4 cm; CF = 3 cm
From ∆ OAE,
OA² = AE² + OE²
⇒ r² = 16 + y²
⇒ y² = r² – 16 ......(i)
From ∆OCF,
(y + 1)² = r² – 9 ..... (ii)
By equation (ii) – (i),
(y + 1)² – y² = r² – 9 – r² + 16
⇒ 2y + 1 = 7
⇒ y = 3 cm
∴ From equation (i),
9 = r² – 16
⇒ r² = 25
⇒ r = 5 cm
Let OE = y cm
then OF = (y +1) cm
OA = OC = r cm
AE = 4 cm; CF = 3 cm
From ∆ OAE,
OA² = AE² + OE²
⇒ r² = 16 + y²
⇒ y² = r² – 16 ......(i)
From ∆OCF,
(y + 1)² = r² – 9 ..... (ii)
By equation (ii) – (i),
(y + 1)² – y² = r² – 9 – r² + 16
⇒ 2y + 1 = 7
⇒ y = 3 cm
∴ From equation (i),
9 = r² – 16
⇒ r² = 25
⇒ r = 5 cm
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AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?.
AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
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AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of AB = 8 cm and CD = 6 cm are two parallel chords on the same side of the centre of a circle. The distance between them is 1 cm. The radius of the circle isa)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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