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:
“Things have their laws, as well as men; and things refuse to be trifled with. Property will be protected.”
—Ralph Waldo Emerson (1803–1882)
“Let the amelioration in our laws of property proceed from the concession of the rich, not from the grasping of the poor. Let us understand that the equitable rule is, that no one should take more than his share, let him be ever so rich.”
—Ralph Waldo Emerson (1803–1882)