Theorem: The measure of an inscribed angle equals one-half the measure of its intercepted arc.

Given: Circle W with inscribed angle BAC, prove that the measure of angle BAC equals the measure of angle BC.

By the way, you need to prove this for three cases.

Case 1: Center W on the interior of angle BAC (as shown above).

Case 2: Center W on the exterior of angle BAC (as shown below).

Case 3: Center W on angle BAC (as shown below).

In each case, try some various auxiliary figures.