The Central Angle Theorem states that the measure of inscribed angle (∠APB) is always half the measure of the central angle ∠AOB. As you adjust the points above, convince yourself that this is true.
This theorem only holds when P is in the major arc. If P is in the minor arc (that is, between A and B) the two angles have a different relationship. In this case, the inscribed angle is the supplement of half the central angle. As a formula: In other words, it is 180 minus what it would normally be.