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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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09 Jun 2022, 06:09
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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.
Total Arcs = 36
i.e. 18 arc should be of length 3 and 18 arc should be of length a
i.e. Circumference of circle \(= 18*3 + 18*a = 18*(3+a) = 2πr\)
Question: a = ?
Statement 1: The central angle that corresponds to the arc of length 3 is 12°
i.e. Total 18 arcs of length 18 represent \(= \frac{18*12}{360} = \frac{3}{5}\) fraction of circle
i.e. \((3/5)*\)Total Circumference \(= 18*3 = 54\) units
remaining circumference i.e. \((2/5)*\)Total Circumference \(= 54*(\frac{5}{3})*(\frac{2}{5}) = 36\) units
i.e. 18a = 36
i.e. a = 2
SUFFICIENT
Statement 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.
Since we dom;t even have the angle at center that all a make hence
NOT SUFFICIENT
Answer: Option A
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