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Rule

Arc Addition Theorem

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
A circle centered at P. Three points on it: A, B, and C.

In the diagram above, the following relation holds true.

Proof

Start by drawing the radii and and by labeling the central angles corresponding to and

A circle centered at P. Three points on it: A, B, and C. Radii PC, PB, and PA. Central angles labeled.
By definition, the arc measure is equal to the measure of the related central angle.
By the Angle Addition Postulate, can be written as the sum of and
Finally, in the above formula, and can be substituted for and respectively.
This theorem is sometimes accepted without a proof. For this reason, it is also known as the Arc Addition Postulate.