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Updated on: 30 May 2023, 09:46
Originally posted by arindamsur on 12 Jun 2014, 02:44.
Last edited by Bunuel on 30 May 2023, 09:46, edited 2 times in total.
Last edited by Bunuel on 30 May 2023, 09:46, edited 2 times in total.
Edited the question
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
45% (01:31) correct
55%
(01:36)
wrong
based on 161
sessions
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A circle, centered at point \(O\) with a radius of \(\frac{2}{\pi}\), has points \(A\) and \(B\) on its circumference. If the length of the minor arc \(AB\) is 0.8 centimeters, what is the degree measure of \(\angle{OAB}\)?
A. 30 Degrees
B. 36 Degrees
C. 48 Degrees
D. 54 Degrees
E. 72 Degrees
M 18 - 34
A. 30 Degrees
B. 36 Degrees
C. 48 Degrees
D. 54 Degrees
E. 72 Degrees
M 18 - 34
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12 Jun 2014, 02:51
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Can you explain me this part.
Now, since arc AB is \(\frac{0.8}{4}=\frac{1}{5}\) of the circumference (360 degrees) then angle AOB is \(\frac{1}{5}\)∗360=72 degrees.
Now, since arc AB is \(\frac{0.8}{4}=\frac{1}{5}\) of the circumference (360 degrees) then angle AOB is \(\frac{1}{5}\)∗360=72 degrees.
12 Jun 2014, 04:24
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A circle, centered at point \(O\) with a radius of \(\frac{2}{\pi}\), has points \(A\) and \(B\) on its circumference. If the length of the minor arc \(AB\) is 0.8 centimeters, what is the degree measure of \(\angle{OAB}\)?
A. 30 degrees
B. 36 degrees
C. 48 degrees
D. 54 degrees
E. 72 degrees
Check the diagram below:
The circumference of the circle is calculated as \(2\pi {r} =2\pi*{\frac{2}{\pi} } = 4\). Given that arc \(AB\) is \(\frac{0.8}{4}=\frac{1}{5}\) of the entire circumference (which is 360 degrees), \(\angle{AOB}\) is therefore \(\frac{1}{5}*360=72\) degrees.
Furthermore, since triangle \(ABO\) is an isosceles triangle (because \(OA=OB=r\)), \(\angle{OAB}\) is therefore \(\frac{180-72}{2}=54\) degrees.
Answer: D
Attachment:
m18-34.png [ 12.6 KiB | Viewed 5965 times ]
