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AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is: (SSC CGL 1st Sit. 2013)
- a)10 cm
- b)11 cm
- c)12 cm
- d)13 cm
Correct answer is option 'D'. 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 = 10 cm and...
To find the radius of the circle, we can use the properties of parallel chords in a circle.
Given:
AB = 10 cm (length of chord AB)
CD = 24 cm (length of chord CD)
Distance between the chords = 17 cm
Let O be the center of the circle, and let E and F be the midpoints of AB and CD, respectively. Since AB and CD are parallel, OE and OF are perpendicular bisectors of AB and CD, respectively.
Using Pythagoras theorem, we can find the length of OE (radius of the circle):
Step 1: Find the length of EF
Since EF is the distance between the chords AB and CD, we have:
EF = CD - AB = 24 cm - 10 cm = 14 cm
Step 2: Find the length of OE
OE is the hypotenuse of right-angled triangle OEF, with EF as the base and OF as the height.
Using Pythagoras theorem, we have:
OE^2 = EF^2 + OF^2
OE^2 = 14 cm^2 + (17/2 cm)^2
OE^2 = 14 cm^2 + 289/4 cm^2
OE^2 = (56 + 289)/4 cm^2
OE^2 = 345/4 cm^2
OE = sqrt(345)/2 cm
Thus, the radius of the circle is sqrt(345)/2 cm, which is approximately equal to 13 cm. Therefore, the correct answer is option D.
Given:
AB = 10 cm (length of chord AB)
CD = 24 cm (length of chord CD)
Distance between the chords = 17 cm
Let O be the center of the circle, and let E and F be the midpoints of AB and CD, respectively. Since AB and CD are parallel, OE and OF are perpendicular bisectors of AB and CD, respectively.
Using Pythagoras theorem, we can find the length of OE (radius of the circle):
Step 1: Find the length of EF
Since EF is the distance between the chords AB and CD, we have:
EF = CD - AB = 24 cm - 10 cm = 14 cm
Step 2: Find the length of OE
OE is the hypotenuse of right-angled triangle OEF, with EF as the base and OF as the height.
Using Pythagoras theorem, we have:
OE^2 = EF^2 + OF^2
OE^2 = 14 cm^2 + (17/2 cm)^2
OE^2 = 14 cm^2 + 289/4 cm^2
OE^2 = (56 + 289)/4 cm^2
OE^2 = 345/4 cm^2
OE = sqrt(345)/2 cm
Thus, the radius of the circle is sqrt(345)/2 cm, which is approximately equal to 13 cm. Therefore, the correct answer is option D.
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Community Answer
AB and CD are two parallel chords of a circle such that AB = 10 cm and...
AB = 10 cm, AE = 5 cm
OE = x
CD = 24 cm, DF = 12 cm
OF = 17 – x
OA = OD = radius
⇒ 52 + x2 = 122 + (17 – x)2
⇒ 25 + x2 = 144 + 289 – 34x + x2
⇒ 34x = 408
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AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is: (SSC CGL 1st Sit. 2013)a)10 cmb)11 cmc)12 cmd)13 cmCorrect answer is option 'D'. Can you explain this answer?
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