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Inscribed Angle of a Circle

Posted: June 14th, 2011, 8:24 pm

an inscribed angle
• vertex lies somewhere on the circle
• sides are chords from the vertex to another point in the circle
• creates an arc, called an intercepted arc
• The measure of the inscribed angle is half of the measure of the intercepted arc

look at the picture above
• $\angle ABC$ is the inscribed angle
• $\overline{BC}$ and $\overline{AC}$ are the chords
• $\widehat{AC}$ is the intercepted arc
• Formula: $\angle ABC=\frac{1}{2}\widehat{AC}$