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AB and CD are two chords of a circle subtending 60° and 120° respectively at the same point on the circumference of the circle. Then AB : CD is
- a)√3 : 1
- b)√2 : 1
- c)1 : 1
- d)√3 : √2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
AB and CD are two chords of a circle subtending 60° and 120° r...
Given information:
- Chords AB and CD subtend angles of 60° and 120° respectively at the same point on the circumference of the circle.
Explanation:
To find the ratio of the lengths of the chords AB and CD, we can use the property that the angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference.
Using this property:
- Angle subtended by chord AB at the center = 2 * 60° = 120°
- Angle subtended by chord CD at the center = 2 * 120° = 240°
Since the sum of the central angles in a circle is 360°, the remaining angles subtended by the chords are:
- Angle subtended by chord AB = 360° - 120° = 240°
- Angle subtended by chord CD = 360° - 240° = 120°
Now, we can use the property that in a circle, the ratio of the lengths of two chords is equal to the ratio of the angles they subtend at the center.
Calculating the ratio:
- Ratio of lengths of chords AB and CD = (angle subtended by AB) : (angle subtended by CD)
- Ratio = 240° : 120°
- Ratio = 2 : 1
Therefore, the correct answer is option (c) 1 : 1.
- Chords AB and CD subtend angles of 60° and 120° respectively at the same point on the circumference of the circle.
Explanation:
To find the ratio of the lengths of the chords AB and CD, we can use the property that the angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference.
Using this property:
- Angle subtended by chord AB at the center = 2 * 60° = 120°
- Angle subtended by chord CD at the center = 2 * 120° = 240°
Since the sum of the central angles in a circle is 360°, the remaining angles subtended by the chords are:
- Angle subtended by chord AB = 360° - 120° = 240°
- Angle subtended by chord CD = 360° - 240° = 120°
Now, we can use the property that in a circle, the ratio of the lengths of two chords is equal to the ratio of the angles they subtend at the center.
Calculating the ratio:
- Ratio of lengths of chords AB and CD = (angle subtended by AB) : (angle subtended by CD)
- Ratio = 240° : 120°
- Ratio = 2 : 1
Therefore, the correct answer is option (c) 1 : 1.
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Community Answer
AB and CD are two chords of a circle subtending 60° and 120° r...
Chords subtending angles at the same point on the circumference of the circle are equal.
∴ AB : CD = 1 : 1.
∴ AB : CD = 1 : 1.
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AB and CD are two chords of a circle subtending 60° and 120° respectively at the same point on the circumference of the circle. Then AB : CD isa)√3 : 1b)√2 : 1c)1 : 1d)√3 : √2Correct answer is option 'C'. Can you explain this answer?
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AB and CD are two chords of a circle subtending 60° and 120° respectively at the same point on the circumference of the circle. Then AB : CD isa)√3 : 1b)√2 : 1c)1 : 1d)√3 : √2Correct answer is option 'C'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about AB and CD are two chords of a circle subtending 60° and 120° respectively at the same point on the circumference of the circle. Then AB : CD isa)√3 : 1b)√2 : 1c)1 : 1d)√3 : √2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are two chords of a circle subtending 60° and 120° respectively at the same point on the circumference of the circle. Then AB : CD isa)√3 : 1b)√2 : 1c)1 : 1d)√3 : √2Correct answer is option 'C'. Can you explain this answer?.
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