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# If the figure above shows part of a circle with arcs of length 3 and

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Math Expert
Joined: 02 Sep 2009
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If the figure above shows part of a circle with arcs of length 3 and  [#permalink]

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13 Sep 2018, 02:32
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Difficulty:

55% (hard)

Question Stats:

72% (01:57) correct 28% (03:13) wrong based on 19 sessions

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If the figure above shows part of a circle with arcs of length 3 and a that alternate around the entire circumference so that there are a total of 36 such arcs, what is the length of one arc of length a?

(1) The central angle that corresponds to the arc of length 3 is 12°.
(2) The portion of the circumference that a occupies is equal to the portion of total degrees in the circle that the central angle that defines a occupies.

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If the figure above shows part of a circle with arcs of length 3 and  [#permalink]

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14 Sep 2018, 12:23
Total circumference = Total 36 segments of both a and 3 = 18a+18*3=18(a+3)

From Statement 1
A central angle is aka angle of the arc = 12°
Formula for Angle of arc = (length/circumference) * 360°
Circumference= (length/angle of arc)*360°
circumference = (3/12)*360 = 90

Circumference = 18(a+3)=90
a+3 =5 => a=2
sufficient A

From statement 2
part a/2 - > The portion of the circumference = length of the arc "a"
Part b/2 - > The portion of total degrees in the circle that the central angle that defines "a" occupies = angle of the arc

length of the arc "a"= angle of the arc = both unknown... so not sufficient

can somebody tell me if my reasoning is right.... thanks in advance
If the figure above shows part of a circle with arcs of length 3 and   [#permalink] 14 Sep 2018, 12:23
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