Property
An inscribed angle is said to intersect an arc on the circle. The arc is the portion of the circle that is in the interior of the angle. The measure of the intercepted arc (equal to its central angle) is exactly twice the measure of the inscribed angle.
This single property has a number of consequences within the circle. For example, it allows one to prove that when two chords intersect in a circle, the products of the lengths of their pieces are equal. It also allows one to prove that the opposite angles of a cyclic quadrilateral are supplementary.
Read more about this topic: Inscribed Angle
Famous quotes containing the word property:
“For experience showed her that she had not, by marrying a man of a large fortune, obtained any great proportion of property which she could call her own or command at her pleasure.”
—Sarah Fielding (1710–1768)
“Man was born rich, or inevitably grows rich by the use of his faculties; by the union of thought with nature. Property is an intellectual proposition.”
—Ralph Waldo Emerson (1803–1882)
“As a man is said to have a right to his property, he may equally be said to have a property in his rights.”
—James Madison (1751–1836)