# What is the Measurement of the Circle O’s Non-Dimensional Chord, MCD?

**What is the Measurement of the Circle O’s Non-Dimensional Chord, MCD?**

The question: “What is the measurement of the circle O’s non-diameter chord, mCD?” may seem to be quite simple. A circle O has two diameters and one non-diameter chord. Each of these chords has a specific length and mAD equals half of the non-diameter chord. However, this simple question doesn’t really answer the question “What is the measurement of the circle O’s two diameters?”

## mCD = 125

If the angle mCD = 125 in circle 0 is equal to 90 degrees, then the central angle BAO equals 180. Similarly, the central angle BOA equals the measure of intercepted arc AD. In this example, the arc AB meets the arc AD at the right angle, resulting in an angle BAO = 90 degrees. This is a right triangle.

Also Read: Graphing Angles – The Pendulum

## mAD = half the measure of the intercepted arc

The length of an arc in a circle is defined by calculating the angle between the central angle (A) and a chord cutting through the center of the circle (B). The radius of a circle and its circumference, called its radius, are the same, and the two radii must have the same scale factor. Thus, mAD = half the measure of the intercepted arc in circle o.

This activity sheet presents a conjecture that mAD is half the measure of an arc in a circle. We know that an angle is right if it is inscribed in a semi-circle. The angle is called an inscribed angle if it has the same intercepted arc as the central arc. Moreover, an inscribed angle has the same measure as the intercepted arc.