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11 Dec 2020, 01:15
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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:
25%
(medium)
Question Stats:
84% (02:01) correct
16%
(01:49)
wrong
based on 44
sessions
History
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Points A, B, and C lie in that order along the circumference of a circle with center O. A second circle with center M has a radius one-third as long as that of the circle with center O. If the area of sector OABC is equal to the area of the circle with center M, then what is the degree measure of \(∠AOC\) ?
A. 30
B. 35
C. 40
D. 45
E. 50
A. 30
B. 35
C. 40
D. 45
E. 50
11 Dec 2020, 01:39
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Given: Points A, B, and C lie in that order along the circumference of a circle with center O. A second circle with center M has a radius one-third as long as that of the circle with center O.
Asked: If the area of sector OABC is equal to the area of the circle with center M, then what is the degree measure of \(∠AOC\) ?
Let the radius of bigger circle be r
Area of sector OABC = Area of circle with centre M =\( \pi (r/3)ˆ2 = \pi rˆ2/9\) = Area of bigger circle /9
Degree measure of \(∠AOC\) = 360/9 = 40
IMO C
Asked: If the area of sector OABC is equal to the area of the circle with center M, then what is the degree measure of \(∠AOC\) ?
Let the radius of bigger circle be r
Area of sector OABC = Area of circle with centre M =\( \pi (r/3)ˆ2 = \pi rˆ2/9\) = Area of bigger circle /9
Degree measure of \(∠AOC\) = 360/9 = 40
IMO C
