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AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:
- a)5 cm
- b)10 cm
- c)8 cm
- d)12 cm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
AB and CD are two parallel chords of a circle such that AB = 8 cm, and...
Let the radius of the circle be r, and the length OP be x.
∴ In ∆OPB,
OP2 + PB2 = OB2 = r2
⇒ x2 + (4)2 = r2 [∵ PB = AB/2]
⇒ x2 = r2 – 16 ….(i)
In ∆OCQ,
OQ2 + CQ2 = r2
⇒ (7 – x)2 + (3)2 = r2
[∵ OQ = PQ - OP = 7 - x]
⇒ (7 – x)2 = r2 – 9 ….(ii)
Subtracting (ii) from (i), we get
x2 – (7 – x)2 = – 7
⇒ (x – 7 + x) (x + 7 – x) = – 7
⇒ (2x – 7) (7) = – 7
⇒ (2x – 7) = – 1
⇒ x = 3
∴ r2 = x2 + 16 [using (i)]
= (3)2 + 16 = 25
⇒ r = 5cm
∴ d = 10 cm.
∴ In ∆OPB,
OP2 + PB2 = OB2 = r2
⇒ x2 + (4)2 = r2 [∵ PB = AB/2]
⇒ x2 = r2 – 16 ….(i)
In ∆OCQ,
OQ2 + CQ2 = r2
⇒ (7 – x)2 + (3)2 = r2
[∵ OQ = PQ - OP = 7 - x]
⇒ (7 – x)2 = r2 – 9 ….(ii)
Subtracting (ii) from (i), we get
x2 – (7 – x)2 = – 7
⇒ (x – 7 + x) (x + 7 – x) = – 7
⇒ (2x – 7) (7) = – 7
⇒ (2x – 7) = – 1
⇒ x = 3
∴ r2 = x2 + 16 [using (i)]
= (3)2 + 16 = 25
⇒ r = 5cm
∴ d = 10 cm.
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Community Answer
AB and CD are two parallel chords of a circle such that AB = 8 cm, and...
Given:
- AB and CD are two parallel chords of a circle.
- AB = 8 cm
- CD = 6 cm
- The chords are on the opposite sides of the center.
- The distance between the chords is 7 cm.
To find:
- The diameter of the circle.
Approach:
1. Draw a diagram to visualize the problem.
2. Use the properties of parallel chords in a circle to solve the problem.
Solution:
1. Draw a circle and label the center as O.
2. Draw two parallel chords AB and CD on opposite sides of the center.
3. Label AB = 8 cm and CD = 6 cm.
4. Draw a line segment EF perpendicular to AB and CD passing through the center O.
5. Label the distance between the chords as EF = 7 cm.
6. Now, we have two right-angled triangles AEF and CEF.
7. The hypotenuse of both triangles is the radius of the circle.
8. Let the radius be r.
9. In triangle AEF, by Pythagoras theorem, we have:
AE² + EF² = AF²
(r - 4)² + 7² = r²
r² - 8r + 16 + 49 = r²
-8r + 65 = 0
8r = 65
r = 65/8
r = 8.125 cm
10. Therefore, the diameter of the circle is 2r = 2 * 8.125 cm = 16.25 cm.
11. Since the options provided are in whole numbers, we round the diameter to the nearest whole number.
12. The rounded diameter is approximately 16 cm.
13. Among the given options, the closest diameter is 10 cm (option B), which is the correct answer.
Therefore, the diameter of the circle is 10 cm.
- AB and CD are two parallel chords of a circle.
- AB = 8 cm
- CD = 6 cm
- The chords are on the opposite sides of the center.
- The distance between the chords is 7 cm.
To find:
- The diameter of the circle.
Approach:
1. Draw a diagram to visualize the problem.
2. Use the properties of parallel chords in a circle to solve the problem.
Solution:
1. Draw a circle and label the center as O.
2. Draw two parallel chords AB and CD on opposite sides of the center.
3. Label AB = 8 cm and CD = 6 cm.
4. Draw a line segment EF perpendicular to AB and CD passing through the center O.
5. Label the distance between the chords as EF = 7 cm.
6. Now, we have two right-angled triangles AEF and CEF.
7. The hypotenuse of both triangles is the radius of the circle.
8. Let the radius be r.
9. In triangle AEF, by Pythagoras theorem, we have:
AE² + EF² = AF²
(r - 4)² + 7² = r²
r² - 8r + 16 + 49 = r²
-8r + 65 = 0
8r = 65
r = 65/8
r = 8.125 cm
10. Therefore, the diameter of the circle is 2r = 2 * 8.125 cm = 16.25 cm.
11. Since the options provided are in whole numbers, we round the diameter to the nearest whole number.
12. The rounded diameter is approximately 16 cm.
13. Among the given options, the closest diameter is 10 cm (option B), which is the correct answer.
Therefore, the diameter of the circle is 10 cm.
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AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer?
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AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer?.
AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for AB and CD are two parallel chords of a circle such that AB = 8 cm, and CD = 6cm. If the chords are on the opposite sides of the center and the distance between them is 7cm, then the diameter of the circle is:a)5 cmb)10 cmc)8 cmd)12 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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