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Updated on: 23 Jun 2013, 01:03
Originally posted by bhandariavi on 09 Feb 2011, 08:35.
Last edited by Bunuel on 23 Jun 2013, 01:03, edited 2 times in total.
Last edited by Bunuel on 23 Jun 2013, 01:03, edited 2 times in total.
Renamed the topic and edited the question.
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Difficulty:
65%
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Question Stats:
59% (02:42) correct
41%
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wrong
based on 198
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In the image shown in the attachment, lines d and l are parallel, and d is a diameter of the circle. d and l intersect the circle at points A and B, and C and D respectively. If the ratio of minor arc CD to arc AB is 1:3, what is the ratio of the length of line l to line d?
A. 1/4
B. 1/3
C. 2/5
D. 1/2
E. π/6
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09 Feb 2011, 08:52
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As AB is a diameter then central angle AOB is straight line = 180 degrees (where O is the center);
Now, as (arc CD)/(arc AB)=1/3 then central angle COD=1/3*180=60 degrees --> triangle COD is equilateral (because CO=DO=radius and <COD=60 degrees) --> CD=r=d/2.
Answer: D.
09 Feb 2011, 08:57
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Arc CD = ϴ/360 x 2πR
Arc AB = 180/360 x 2πR
Arc CD/Arc AB = ϴ/180
ϴ/180 = 1/3 or ϴ = 60
Now triangle OCD (where O is the centre)
OC = OD = R [Radius]
Thus angle OCD = angle CDO = x
In Triangle OCD
x + x + 60 = 180
or x = 60
Yipeee! The triangle is an equilateral triangle! So CD = R
AB = 2R
So CD/AB = 1/2
Arc AB = 180/360 x 2πR
Arc CD/Arc AB = ϴ/180
ϴ/180 = 1/3 or ϴ = 60
Now triangle OCD (where O is the centre)
OC = OD = R [Radius]
Thus angle OCD = angle CDO = x
In Triangle OCD
x + x + 60 = 180
or x = 60
Yipeee! The triangle is an equilateral triangle! So CD = R
AB = 2R
So CD/AB = 1/2
