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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