If A, B and C are three distinct points on a circle, the angle BAC^\widehat{BAC} (in blue) is an inscribed angle. We also say that this angle subtends the arc BC^\widehat{BC}. If O is the center of the circle, the angle BOC^\widehat{BOC} (in red) is the central angle subtending the same arc BC^\widehat{BC}.
The two configurations, according to whether the inscribed angle is acute or obtuse.
From the central angle theorem to the inscribed angle theorem ====================================================================
The key result here is the inscribed angle theorem. It has two versions, depending on whether geometric or oriented angles are used. Begin with the classical version, which uses the definition of a central angle given above: