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AB = 8 cm and CD = 6 cm are parallel chords on the same side of the centre of a circle. The distance between them is 1cm. 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?
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Verified Answer
AB = 8 cm and CD = 6 cm are parallel chords on the same side of the c...
Let OE= x
OF = x+1, OA=OC= r
AE= 4cm, CF= 3cm
From ∆ OAE
r2 = 16+x2
x2 = r2- 16 ------(1)
From ∆ OCF
(x+1)2 = r2 - 9 ------ (2)
By equation (2) - (1)
x = 3cm
r = 5cm
Most Upvoted Answer
AB = 8 cm and CD = 6 cm are parallel chords on the same side of the c...
Given information:
AB = 8 cm
CD = 6 cm
Distance between AB and CD = 1 cm
Formula:
In a circle, parallel chords equidistant from the center are of equal length.
Calculation:
- Since AB and CD are parallel chords on the same side of the center of the circle, and the distance between them is 1 cm, we can conclude that the perpendicular distance from the center of the circle to each chord is 0.5 cm.
- Let O be the center of the circle, and let E be the midpoint of AB.
- In triangle AOE, AE is the hypotenuse, and AO and OE are the perpendicular distances from the center to the chord and the midpoint of the chord respectively.
- Using the Pythagorean theorem, we can find the radius of the circle:
AO^2 + OE^2 = AE^2
(r - 0.5)^2 + (4)^2 = (r + 0.5)^2
r^2 - r + 0.25 + 16 = r^2 + r + 0.25
2r = 16
r = 8 cm
Therefore, the radius of the circle is 5 cm (Option A).
AB = 8 cm
CD = 6 cm
Distance between AB and CD = 1 cm
Formula:
In a circle, parallel chords equidistant from the center are of equal length.
Calculation:
- Since AB and CD are parallel chords on the same side of the center of the circle, and the distance between them is 1 cm, we can conclude that the perpendicular distance from the center of the circle to each chord is 0.5 cm.
- Let O be the center of the circle, and let E be the midpoint of AB.
- In triangle AOE, AE is the hypotenuse, and AO and OE are the perpendicular distances from the center to the chord and the midpoint of the chord respectively.
- Using the Pythagorean theorem, we can find the radius of the circle:
AO^2 + OE^2 = AE^2
(r - 0.5)^2 + (4)^2 = (r + 0.5)^2
r^2 - r + 0.25 + 16 = r^2 + r + 0.25
2r = 16
r = 8 cm
Therefore, the radius of the circle is 5 cm (Option A).
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AB = 8 cm and CD = 6 cm are parallel chords on the same side of the centre of a circle. The distance between them is 1cm. The radius of the circle is:a)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?
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AB = 8 cm and CD = 6 cm are parallel chords on the same side of the centre of a circle. The distance between them is 1cm. The radius of the circle is:a)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about AB = 8 cm and CD = 6 cm are parallel chords on the same side of the centre of a circle. The distance between them is 1cm. The radius of the circle is:a)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB = 8 cm and CD = 6 cm are parallel chords on the same side of the centre of a circle. The distance between them is 1cm. The radius of the circle is:a)5 cmb)4 cmc)3 cmd)2 cmCorrect answer is option 'A'. Can you explain this answer?.
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