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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
Posts: 55271
If the figure above shows part of a circle with arcs of length 3 and  [#permalink]

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13 Sep 2018, 02:31
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Difficulty:

55% (hard)

Question Stats:

58% (01:34) correct 42% (01:47) wrong based on 14 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 degree measure of one arc of length a?

(1) The circumference of the circle is 90.
(2) The length of a is 2.

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image012.jpg [ 2.08 KiB | Viewed 374 times ]

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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, 03:16
1
Bunuel wrote:

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 degree measure of one arc of length a?

(1) The circumference of the circle is 90.
(2) The length of a is 2.

Attachment:
image012.jpg

36 such arcs i.e. 18 arcs of length 3 and 18 arcs of length a
i.e. Total Circumference$$= 18*(a+3) = 18a+54$$

Question: Degree measure of arc of length a = ?

Statement 1: The circumference of the circle is 90.
i.e. $$18*(a+3) = 18a+54=90$$
now $$(Angle/360) = 36/90$$
i.e. Angle for all $$18a = 144$$
i.e. angle of $$a = 8º$$
SUFFICIENT

Statement 2: The length of a is 2
Using this also total circumference can be calculated
as $$18a+54 = 18*2+54 = 90$$
i.e. now $$(Angle/360) = 36/90$$
i.e. Angle for all $$18a = 144$$
i.e. angle of $$a = 8º$$
SUFFICIENT

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If the figure above shows part of a circle with arcs of length 3 and   [#permalink] 13 Sep 2018, 03:16
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