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:
“The property of rain is to wet and fire to burn.”
—William Shakespeare (1564–1616)
“It is clearly better that property should be private, but the use of it common; and the special business of the legislator is to create in men this benevolent disposition.”
—Aristotle (384–322 B.C.)
“Oh, had I received the education I desired, had I been bred to the profession of the law, I might have been a useful member of society, and instead of myself and my property being taken care of, I might have been a protector of the helpless, a pleader for the poor and unfortunate.”
—Sarah M. Grimke (1792–1873)