Central Angle of a Circle Formula. A central angle is formed between two radii of a circle where two points intersect and form a segment, and the distance between points is the arc length that is denoted by l in geometry. A central formed at the center of the circle where two radii meet or intersect. Or this could be taken as the angle subtended at a specific point on the circle by two other points. In brief, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem is related to the measure of an inscribed angle to the central angle subtending over the same arc.

Length of a Circular Arc: (with central angle ) if the angle is in degrees, then length = x (PI/180) x r if the angle is in radians, then length = r x. Area of Circle Sector: (with central angle ) if the angle is in degrees, then area = (/360)x PI r 2 Because one-fourth of the circle is shaded, we just multiply the area formula of circle c by a factor of ¼ to find the area of the circle sector. In other cases, we may be given the measure of the angle at the radius of a circle, called the central angle. For those exercises, we can apply the area of sectors formula, which is