Arc Addition Theorem

Start by drawing the radii PA, PB, and PC, and by labeling the central angles corresponding to AB, BC, and ABC.

By definition, the arc measure is equal to the measure of the related central angle. m AB &= m∠ 1 m BC &= m∠ 2 mABC&=m∠ 3 By the Angle Addition Postulate, m∠ 3 can be written as the sum of m∠ 1 and m∠ 2. mABC = m∠ 3 ⇕ mABC = m∠ 1+m∠ 2 Finally, in the above formula, m AB and m BC can be substituted for m∠ 1 and m∠ 2, respectively. mABC = m∠ 1+m∠ 2 ⇕ mABC = m AB + m BC