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:
“No man is by nature the property of another. The defendant is, therefore, by nature free.”
—Samuel Johnson (1709–1784)
“I must feel pride in my friend’s accomplishments as if they were mine,—and a property in his virtues. I feel as warmly when he is praised, as the lover when he hears applause of his engaged maiden.”
—Ralph Waldo Emerson (1803–1882)
“When a strong man, fully armed, guards his castle, his property is safe. But when one stronger than he attacks him and overpowers him, he takes away his armor in which he trusted and divides his plunder.”
—Bible: New Testament, Luke 11:21.22.