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In the image shown in the attachment, lines d and l are para [#permalink]

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09 Feb 2011, 07:35

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63% (01:57) correct 37% (01:36) wrong based on 134 sessions

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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?

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? Choices A. 1/4 B. 1/3 C. 2/5 D.1/2 E. π/6

Attachment:

untitled.PNG [ 8.6 KiB | Viewed 2728 times ]

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.

Re: In the image shown in the attachment, lines d and l are para [#permalink]

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18 Jul 2014, 02:50

As the arc length is 1/3 of the semicircle , divide the semicircle in to 3 equal regions. You will now see that the angle at the center is 180/3 = 60 and also the triangle in the center will be equilateral as the two sides are equal as they are both radius of the circle.

You can now get the ratio as radius/diameter = 1/2 (Option D)

Re: In the image shown in the attachment, lines d and l are para [#permalink]

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05 Jan 2018, 17:33

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