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14 Sep 2018, 01:27
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (02:11) correct
39%
(02:10)
wrong
based on 128
sessions
History
Date
Time
Result
Not Attempted Yet
If the length of the arc ACB in the circle above with center O is 12π, and the radius of the circle is 15, what is the measure of the angle OAD in degrees?
A. 12
B. 18
C. 24
D. 36
E. 72
Attachment:
image007.jpg [ 2.42 KiB | Viewed 2722 times ]
14 Sep 2018, 01:43
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Bunuel
Arc ACB=12\(\pi\)
r=15
circumference=2\(\pi\) x 15=30\(\pi\)
\(\angle\)AOB = \(\frac{12\pi}{30\pi}\)x360 = 144
\(\angle\) AOD=180-144=36
\(\angle\) ODA= \(\angle\) OAD = \(\frac{144}{2}\)=72
Answer E.
17 Jul 2020, 22:26
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Bunuel
Radius of the circle = 15
=> Circumference = 2πr = 2 * 15 * π = 30π
Now,
30π corresponds an angle of 360°.
=> 1π corresponds an angle of \(\frac{360}{30}\) = 12°
=> 12π corresponds an angle of 12 * 12 = 144°
Therefore \(∠AOB\) = 144°
Now,
\(∠AOB\) + \(∠AOD\) = 180°
=> \(144° \)+ \(∠AOD\) = 180°
=> \(∠AOD\) = \(36°\)
Now, \(OA\) = \(OD\) (Because both are radius of the same circle)
=> \(∠OAD\) = \(∠ODA \) (Isosceles triangle)
\( Let ∠OAD = x\)
Therefore,
\(∠AOD\) + x + x = \(180°\) (Angle sum property of a triangle)
=> \(2x\) = 180° - 36° = 144°
=> x = \(\frac{144°}{2}\) = \(72°\)
Hence, OA is (E)
02 Aug 2022, 12:34
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