The ongoing cycle

Central Angle



The angle subtended at the center of a circle by two given points on the circle.Central angle is an angle formed by two rays from the center of a circle, with the center forming the vertex. A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is (by definition) equal to the central angle itself. It is also known as the arc segment’s angular distance.

There are several different angles associated with circles. Perhaps the one that most immediately comes to mind is the central angle. It is the central angle’s ability to sweep through an arc of 360 degrees that determines the number of degrees usually thought of as being contained by a circle. The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle It also says that the measure of the minor arc is equal to the measure of a central angle.

Inscribed Angle

Definition: The angle subtended at a point on the circle by two given points on the circle. Try this Drag any orange dot. Note that when moving the point P, the inscribed angle is constant while it is in the major arc formed by A,B. (If there is no image below, see support page.) Java plug-in Version 1.4 or later required. Given two points A and B, lines from them to a third point P form the inscribed angle ∠APB. As you drag the point P above, notice that the inscribed angle is constant. It only depends on the position of A and B. The inscribed angle is only defined for points on the major arc (the longest path around the circle between the two given points). In the figure above, if you drag P around into the shorter (minor) arc it will be undefined. Formula for inscribed angle If you know the length of the minor arc and radius, the inscribed angle is: where: L is the length of the minor (shortest) arc AB R is the radius of the circle π is Pi, approximately