2. Finding Arc Measures
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Begin by considering a central angle and its circular arc.
See solution.
To talk about how circular arcs are measured, we have to understand the meaning of central angle and a circular arc. Let's first recall the definition of a central angle.
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An angle is called a central angle if and only if its vertex lies on the center of the circle. |
Consider a circle with center O. Let A and B be two points on the circle. Therefore, ∠AOB is a central angle of ⊙ O.
A circular arc, on the other hand, can be defined as a proportion of a circle defined by a central angle. In the above figure, AB is a circular arc.
How are a circular arc and its central angle related? The measure of a circular arc is the measure of its central angle. Considering the above figure, we can say that AB and ∠AOB have the same measure. mAB= m ∠AOB Therefore, we can conclude that circular arcs are measured by using their central angles.