## adjacent arcs

### Adjacent arcs refer to two arcs in a circle that have the same center and share a common endpoint

Adjacent arcs refer to two arcs in a circle that have the same center and share a common endpoint. The common endpoint of the arcs is known as the vertex of the arcs.

In order to understand adjacent arcs, let’s consider a circle with center O. If we have two arcs, say arc AB and arc BC, where A, B, and C lie on the circle, then arc AB and arc BC are adjacent if they share the endpoint B and have their other endpoints at points A and C, respectively. So, the arcs AB and BC are adjacent because they share a common endpoint B and have the same center O.

It is important to note that for two arcs to be adjacent, they must be part of the same circle or congruent circles. Also, adjacent arcs are always non-overlapping, meaning that they do not intersect each other inside the circle. However, they may touch or share an endpoint.

Adjacent arcs are frequently used in geometry and trigonometry when dealing with angles and angle measures. The measure of an angle formed by adjacent arcs is equal to half of the difference between the measures of the arcs. This concept is utilized in solving problems involving arc lengths, sector areas, and central angles in circles.

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