Inscribed and Central Angles in Circles
Definitions and theorems related to inscribed and central angles in circles are discussed using examples. See also interactive tutorial on central and inscribed angles.
Definitions1 - A central angle of a circle is an angle whose vertex is located at the center of the circle. Angle BOC in the figure below.2 - An inscribed angle is an angle whose vertex is on a circle and whose sides each intersect the circle at another point. Angle CAB in the figure below.
Theorem1 - An inscribed angle is half the measure of the central angle intercepting the same arc.2 - Two or more inscribed angles intercepting the same arc are equal.
ProblemIn the figure below chord CA has a length of 12 cm. The circle of center O has a radius of 14 cm. Find an approximate value (2 decimal places) to the size of the inscribed angle CBA.Solution to Problem 1
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