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:
“A few days later the younger son gathered all he had and traveled to a distant country, and there he squandered his property in dissolute living.”
—Bible: New Testament, Luke 15:13.
“It is better to write of laughter than of tears, for laughter is the property of man.”
—François Rabelais (1494–1553)
“Things have their laws, as well as men; and things refuse to be trifled with. Property will be protected.”
—Ralph Waldo Emerson (1803–1882)