Intercepted Arc: Definition & Formula

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Lesson Transcript
Instructor: Ellen Manchester
Very often, as we look around our world, we see parts of circles. In this lesson, we will take a look at the arc that runs along the circumference of the circle in between the two chords, called the intercepted arc.

The Intercepted Arc: What Is It?

An intercepted arc is an interesting term. This arc has a very close relationship with the angles that encompass the arc. The intercepted arc is a section of the circumference of a circle. It is encased on either side by two different chords or line segments that meet at one point, called a vertex, on the other side of the circle or in the middle of the circle. The angle formed by these two chords or line segments is called an inscribed angle or a central angle depending on where the vertex lies.

Intercepted Arc vs. Inscribed Angle
Intercepted arc vs. inscribed angle

Interceped Arc vs. Central Angle
Intercepted arc vs. central angle

The Relationship Between the Intercepted Arc and the Inscribed Angle

The intercepted arc has a very close relationship with the inscribed angle. The inscribed angle is an angle formed by the vertex on the circle and chords forming the angle. Since the inscribed angle has a degree measure, the intercepted arc also has a degree measure. The intercepted arc is twice the size of the inscribed angle. For instance, if we had a 50 degree inscribed angle, the intercepted arc would have a measure of 100 degrees, 50 degrees * 2 = 100 degrees. Take a look at this intercepted arc:

Intercepted Arc 100-degree

When you have an inscribed angle of 30 degrees, what do you think the intercepted arc would measure? 30 * 2 = 60 degrees.

Intercepted arc 60-degree

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