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29 Oct 2019, 02:25
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
81% (00:49) correct
19%
(01:18)
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based on 58
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What is the radius of the circle above with center O?
(1) The measure of the angle ABC is 30°.
(2) The length of the arc AC is 2.
Attachment:
image006.gif [ 2.21 KiB | Viewed 1507 times ]
29 Oct 2019, 02:34
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Bunuel
What is the radius of the circle above with center O?
(1) The measure of the angle ABC is 30°.
(2) The length of the arc AC is 2.
Attachment:
image006.gif
Asked: What is the radius of the circle above with center O?
(1) The measure of the angle ABC is 30°.
angle ACO = 2*30 = 60
Since 2 sides of triangle OA & OC are radius; angles OCA & OAC are equal and 60.
Triangle ACO is equilateral triangle.
Since no length is provided.
NOT SUFFICIENT
(2) The length of the arc AC is 2.
Since there is no information provided about angle AOC.
NOT SUFFICIENT
(1) + (2)
(1) The measure of the angle ABC is 30°.
(2) The length of the arc AC is 2.
Angle AOC = 2 * 30 = 60
Circumference of the circle = \(360/60 * 2 = 6 *2 = 12 = 2\pi r\)
Radius of circle r \(= 6/\pi\)
SUFFICIENT
IMO C
Statement1: Angle ABC = 30, hence, Angle AOC = 60
AO = OC = r(radius) hence, Angle OAC and Angle OCA are equal (isoceles angles)
Angle O + Angle A + Angle C = 180
Angle A = Angle C = 60 (since Angle O = 60)
triangle AOC is an equilateral triangle
Hence, AC = OC = AO = r
Since we don't know anything about the length any of the side, hence INSUFFICIENT
Statement2: AC = 2
Since we do not have any information regarding any angle or the relation between the sides, this statement alone is INSUFFICIENT
Statement 1 & Statement 2:
From statement 1, we know that AC = OA = OC = r(radius)
and from statement 2, we know Arc length AC = 2
So, \(r = \frac{6}{pie}\)
SUFFICIENT
Option C
AO = OC = r(radius) hence, Angle OAC and Angle OCA are equal (isoceles angles)
Angle O + Angle A + Angle C = 180
Angle A = Angle C = 60 (since Angle O = 60)
triangle AOC is an equilateral triangle
Hence, AC = OC = AO = r
Since we don't know anything about the length any of the side, hence INSUFFICIENT
Statement2: AC = 2
Since we do not have any information regarding any angle or the relation between the sides, this statement alone is INSUFFICIENT
Statement 1 & Statement 2:
From statement 1, we know that AC = OA = OC = r(radius)
and from statement 2, we know Arc length AC = 2
So, \(r = \frac{6}{pie}\)
SUFFICIENT
Option C
