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16 Sep 2014, 01:04
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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
A. 30 degrees
B. 36 degrees
C. 48 degrees
D. 54 degrees
E. 72 degrees
16 Sep 2014, 01:04
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Official Solution:
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
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
30 Aug 2016, 05:06
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I think this is a high-quality question and I agree with explanation.
