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Question Video: Finding the Measure of an Arc Given Its Equal Arc’s Measure Mathematics

Find π‘š arc 𝐡𝐸, where 𝑀 is the center of the circle.

01:22

Video Transcript

Find the measure of arc 𝐡𝐸, where 𝑀 is the center of the circle.

First, let’s identify arc 𝐡𝐸. After we highlight arc 𝐡𝐸, it’s important to notice that the segment 𝐡𝐴 and the segment 𝐸𝐢 are two parallel chords in this circle. We know by the measures of arcs between parallel chords theorem that the measure of the arcs between parallel chords of a circle are equal. This means that the arc 𝐡𝐸 will be equal in measure to the arc 𝐴𝐢. We can also see that line segment 𝐷𝐢 intersects line segment 𝐡𝐴 at the center of the circle 𝑀.

We can therefore say that angle 𝐴𝑀𝐢 is the opposite or vertical angle from angle 𝐡𝑀𝐷 and is, therefore, also equal to 39 degrees. Since 𝑀 is the center of the circle and arc 𝐴𝐢 is subtended by the angle 𝐴𝑀𝐢, we can say that the arc measure is equal to the central angle measure, which is 39 degrees. Since arc 𝐴𝐢 is 39 degrees, arc 𝐡𝐸 must also be equal to 39 degrees.

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