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ABCDEF is a regular hexagon inscribed in circle O

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Carcass
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ABCDEF is a regular hexagon inscribed in circle O [#permalink] New post   30 Dec 2020, 11:08
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Attachment:
gre ABCDEF is a regular hexagon inscribed in circle.jpg
gre ABCDEF is a regular hexagon inscribed in circle.jpg [ 15.44 KiB | Viewed 7948 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
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Re: ABCDEF is a regular hexagon inscribed in circle O [#permalink] New post   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
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Re: ABCDEF is a regular hexagon inscribed in circle O [#permalink] New post   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.
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Re: ABCDEF is a regular hexagon inscribed in circle O [#permalink] New post   16 Dec 2022, 19:52
pretend that the diameter of the circle = 10 thus the radius (QA) equals 5
The length of an arc = X/360 * 2*Pi*R (where x is the measure of the angle in question)
if the shape is a regular hexagon then each the internal angles are 720 degree ((6-2) * 180)
720 / 6 = 120
120 / 360 * 2 * pi * 5 (the radius we established earlier) = 3.3333333 * pi > 5
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Re: ABCDEF is a regular hexagon inscribed in circle O [#permalink]
16 Dec 2022, 19:52
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