## Inscribed Angle

### An inscribed angle is an angle that is formed by two chords in a circle, with its vertex at the center of the circle

An inscribed angle is an angle that is formed by two chords in a circle, with its vertex at the center of the circle. The two chords intersect at two points on the circle, and the angle is created by connecting these two points with the center of the circle. The inscribed angle is said to be “inscribed” because its vertex is located on the circumference of the circle.

The measure of an inscribed angle is equal to half the measure of its intercepted arc. This means that if we know the measure of the intercepted arc, we can find the measure of the inscribed angle by simply dividing it in half.

There are a couple of notable properties of inscribed angles. First, two inscribed angles that intercept the same arc are congruent. This means that if two angles have their vertices on the same arc, their measures will be equal.

Another important property is that an inscribed angle is always equal to the opposite angle formed by the same two chords. In other words, if we have an angle formed by two chords in a circle, and we also have an angle formed by the same two chords but with its vertex on the circumference of the circle, these two angles will be equal in measure.

Inscribed angles play a significant role in many geometric problems involving circles, such as finding the length of a chord or determining the relationships between different angles formed by chords.

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