The circumference of the circle with center O shown above is 15 π. L M N O is a parallelogram an

step 1 Here's a sketch of the figure. We have a circle and a parallelogram, and we're told that the mea

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

The circumference of the circle with center $O$ shown above is $15 \pi . L M N O$ is a parallelogram and $\angle O L M=108^{\circ} .$ What is the length of minor arc $A B ?$
a. $15 \pi$
b. $9 \pi$
c. $3 \pi$
d. $2 \pi$
e. $\pi$

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Key Concepts

Circumference of a Circle

The circumference is the total distance around a circle and is calculated using the formula C = 2?r. Knowing the circumference allows one to determine the radius of the circle, which is a foundational aspect of circle geometry.

Arc Length

Arc length is the distance along a segment of the circle's perimeter. It is directly related to the central angle that intercepts the arc. The arc length can be calculated by (?/360°) × C when the angle is in degrees, establishing a proportional relationship between the angle and the circumference.

Central Angles

A central angle is an angle with its vertex at the center of the circle, and it intercepts an arc on the circle. The measurement of the central angle determines the proportion of the circle’s circumference that the intercepted arc represents.

Properties of Parallelograms

Parallelograms are quadrilaterals with opposite sides that are both parallel and equal in length, and their angles have specific relationships. These properties are important when the quadrilateral is combined with circle geometry, as they can help deduce unknown angle measures that relate to circle arcs and other geometric elements.

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