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Chords in a circle

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by shankar.ashwin » Thu Sep 15, 2011 2:45 am
What is the maximum number of chords with length 'R' which can be drawn in a circle with radius 'R', such that no two chords intersect inside the circle.

A) 2
B) 4
C) 6
D) 8
E) None of these
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by cans » Thu Sep 15, 2011 3:17 am
IMO A
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by GMATGuruNY » Thu Sep 15, 2011 3:18 am
shankar.ashwin wrote:What is the maximum number of chords with length 'R' which can be drawn in a circle with radius 'R', such that no two chords intersect inside the circle.

A) 2
B) 4
C) 6
D) 8
E) None of these
Image

The 6 possible chords form the hexagon shown above.

The correct answer is C.
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by cans » Thu Sep 15, 2011 4:34 am
But don't they intersect? (They share a common end point)
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by shankar.ashwin » Thu Sep 15, 2011 4:38 am
Hi Cans, the OA is 6.
They mention in the question that the chords should not intersect inside the circle. 2 chords meeting at the circumference, they do not actually intersect.

The problem tests us on the concept that 6 eq. triangles with side 'a' constitute a hexagon which can be inscribed inside a circle of radius 'a'.

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cans wrote:But don't they intersect? (They share a common end point)
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by GMATGuruNY » Thu Sep 15, 2011 6:21 am
cans wrote:But don't they intersect? (They share a common end point)
Yes, but they intersect ON the circle, so they satisfy the condition that no two chords intersect INSIDE the circle.
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by sam2304 » Thu Sep 15, 2011 10:32 am
If that is the case then an octagon inscribed in a circle will have 8 chords and they won't intersect as well. It can be more as well say a 10 sided figure in a circle. Draw 15 parallel lines in a circle, each of them are chords and none of them will intersect each other. So shouldn't it be none of these. As a matter of fact a circle can have infinite number of chords not intersecting each other. Correct me if i am wrong.
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by sam2304 » Thu Sep 15, 2011 10:34 am
Extremely sorry :(. My bad i din't notice the length R equal to radius mentioned in the problem. :)
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by bubbliiiiiiii » Fri Sep 16, 2011 12:40 am
GMATGuruNY wrote:
shankar.ashwin wrote:What is the maximum number of chords with length 'R' which can be drawn in a circle with radius 'R', such that no two chords intersect inside the circle.

A) 2
B) 4
C) 6
D) 8
E) None of these
Image

The 6 possible chords form the hexagon shown above.

The correct answer is C.
Is this an established theorm?

I mean should we make note of this point remember for future problems?
Regards,

Pranay
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