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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Chords in a circle
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shankar.ashwin
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cans
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IMO A
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GMATGuruNY
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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
The 6 possible chords form the hexagon shown above.
The correct answer is C.
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cans
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But don't they intersect? (They share a common end point)
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shankar.ashwin
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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'.
Tricky sum
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'.
Tricky sum
cans wrote:But don't they intersect? (They share a common end point)
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GMATGuruNY
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Yes, but they intersect ON the circle, so they satisfy the condition that no two chords intersect INSIDE the circle.cans wrote:But don't they intersect? (They share a common end point)
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sam2304
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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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sam2304
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Extremely sorry 
. My bad i din't notice the length R equal to radius mentioned in the problem. 
. My bad i din't notice the length R equal to radius mentioned in the problem. Getting defeated is just a temporary notion, giving it up is what makes it permanent.
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bubbliiiiiiii
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Is this an established theorm?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
The 6 possible chords form the hexagon shown above.
The correct answer is C.
I mean should we make note of this point remember for future problems?
Regards,
Pranay
Pranay
