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ABCDEF is a regular hexagon inscribed in circle O
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30 Dec 2020, 11:08
30 Dec 2020, 11:08
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Question Stats:
61% (01:19) correct
38% (01:12) wrong based on 152 sessions
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gre ABCDEF is a regular hexagon inscribed in circle.jpg [ 15.44 KiB | Viewed 10591 times ]
\(ABCDEF\) is a regular hexagon inscribed in circle O
\(\overline{AD} \) is a diameter of circle O
Quantity A |
Quantity B |
The length of radius \(\overline{OD}\) |
The length of arc \(\widehat{FE}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: ABCDEF is a regular hexagon inscribed in circle O
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01 Jan 2021, 08:19
01 Jan 2021, 08:19
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AD is the diameter hence OD will be radius.
The hexagon is regular so all sides will be equal.
Triangle OBC will form an equilateral triangle.
OB = OC = BC = radius
Qt A
Radius OD = BC = EF = side of hexagon
Qt B
The length of arc \(\widehat{FE}\)
This can be calculated as = \(\frac{angle EOF}{360} * 2 * pi * radius\)
= \(\frac{60}{360} * 2 * pi * EF\)
= \(\frac{pi}{3} * EF\)
= 1.046 * EF
So Qt B > Qt A
Answer B
The hexagon is regular so all sides will be equal.
Triangle OBC will form an equilateral triangle.
OB = OC = BC = radius
Qt A
Radius OD = BC = EF = side of hexagon
Qt B
The length of arc \(\widehat{FE}\)
This can be calculated as = \(\frac{angle EOF}{360} * 2 * pi * radius\)
= \(\frac{60}{360} * 2 * pi * EF\)
= \(\frac{pi}{3} * EF\)
= 1.046 * EF
So Qt B > Qt A
Answer B
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Re: ABCDEF is a regular hexagon inscribed in circle O
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03 Jun 2021, 04:15
03 Jun 2021, 04:15
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Carcass wrote:
Attachment:
gre ABCDEF is a regular hexagon inscribed in circle.jpg
\(ABCDEF\) is a regular hexagon inscribed in circle O
\(\overline{AD} \) is a diameter of circle O
Quantity A |
Quantity B |
The length of radius \(\overline{OD}\) |
The length of arc \(\widehat{FE}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
We are told that hexagonal is inscribed inside the circle, the basic property of hexagonal states its consists 6 equilateral triangle.
Hence all side of the given triangle are equal.
But,
radius OD is straight line segment and FE is curve path,
Hence, FE is greater.
