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The circumference of the circle with center O shown above is 15. LMNO

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The circumference of the circle with center O shown above is 15. LMNO [#permalink] New post   12 Jun 2023, 09:32
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The circumference of the circle with center O shown above is 15π. LMNO is a parallelogram and ∠OLM = 108°. What is the length of minor arc AB ?

A. 15π
B. 9π
C. 3π
D. 2π
E. π


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C
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Midhilesh489
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Re: The circumference of the circle with center O shown above is 15. LMNO [#permalink] New post   13 Jun 2023, 09:13
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Angle AOB = 72

Length of arc = 72/360 * 15pi = 3pi
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Re: The circumference of the circle with center O shown above is 15. LMNO [#permalink] New post   13 Jun 2023, 14:21
1
Angle OLM= 108°
So, Angle LON= Angle AOB = 180-108= 72°

Now, 72/360=1/5
So, arc AB is 1/5 the circumference
arc AB = (1/5)*15π= 3π
Ans: C

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Re: The circumference of the circle with center O shown above is 15. LMNO [#permalink] New post   14 Jun 2023, 04:00
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OE


The interior angles of a parallelogram add up to 360°, and
two adjacent angles of a parallelogram add up to 180°. Angle
OLM = 108°, which means that angle AOB = 180° − 108° =
72°. The ratio of a central angle to 360° is equal to the ratio
of the arc defined by the central angle to the circumference,
which is 15π. So 72°/360°=Minor ARC AB/15π which means that arc AB=72°*15n/360°=3n

C is the correct option
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