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Find π arc π΅πΈ, where π is the center of the circle.

Find the measure of arc π΅πΈ, where π is the center of the circle.

First, letβs identify arc π΅πΈ. After we highlight arc π΅πΈ, itβs important to notice that the segment π΅π΄ and the segment πΈπΆ 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 π΅πΈ will be equal in measure to the arc π΄πΆ. We can also see that line segment π·πΆ intersects line segment π΅π΄ at the center of the circle π.

We can therefore say that angle π΄ππΆ is the opposite or vertical angle from angle π΅ππ· and is, therefore, also equal to 39 degrees. Since π is the center of the circle and arc π΄πΆ is subtended by the angle π΄ππΆ, we can say that the arc measure is equal to the central angle measure, which is 39 degrees. Since arc π΄πΆ is 39 degrees, arc π΅πΈ must also be equal to 39 degrees.

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