![]() mAOB 82 In a circle, or congruent circles, congruent central angles have congruent arcs. Central Angle Intercepted Arc In the diagram at the right, AOB is a central angle with an intercepted minor arc from A to B. The angle will vary in case of isosceles triangle. Central Angle A central angle is an angle formed by two radii with the vertex at the center of the circle. ![]() The two sides which are the radii are labelled r. ![]() Note: If the question was given for isosceles triangle instead of equilateral triangle, the OA$\ne $OB$\ne $OC $\ne $radius. Since the circle is a mirror image vertically, Ive only drawn in the top half of the interior shape. So, OB and OC are bisectors of $\angle B$ and $\angle C$ respectively.įor an Equilateral triangle all angles as $60$īecause $\Delta OBD$ is equal to $\Delta ODC.$ Let OD be a perpendicular from 0 to side BC. OA, OB and OC correspond to the radius of the circle. The central angle theorem states that the central angle from two chosen points on the circle is always twice the inscribed angle from those two points. ![]()
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