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08 Jun 2022, 03:45
Kudos
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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:
35%
(medium)
Question Stats:
64% (02:01) correct
36%
(02:02)
wrong
based on 28
sessions
History
Date
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Not Attempted Yet
If the measure of the angle ADO is 50°, and the radius is 9 what is the length of the arc ACB?
A. 2π
B. 3π
C. 5π
D. 6π
E. 8π
Attachment:
image008 (2).jpg [ 2.42 KiB | Viewed 1735 times ]
08 Jun 2022, 06:43
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Bunuel
If ADO is 50 degrees, DAO is also 50 degrees. That makes AOD 80 degrees, so AOB is 100 degrees.
The total circumference is 18pi. The arc we want is just barely more than one quarter of the circle. One quarter of the circle is 4.5pi.
Answer choice C.
If you don't like the "just barely" approach, my first suggestion is to get comfortable with (and good at!) ballparking. We only have five answer choices, so if four of them aren't close to what we want, we can get the right answer without always doing all of the math. It didn't save us a ton of time on this question, but it's a really useful skill to master. If that's not satisfying to you, 4.5pi is 90 degrees of the circle. We want 100 degrees, so we need \(1\frac{1}{9}*4.5pi\). 1/9 of 4.5pi is 0.5pi. 4.5pi +0.5pi = 5pi.
14 Jun 2022, 02:41
Kudos
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Can you please explain how DAO is 50 as well? Are we assuming that DB is the diameter?
