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 power of perpetuating our property in our families is one of the most valuable and interesting circumstances belonging to it, and that which tends the most to the perpetuation of society itself.”
—Edmund Burke (1729–1797)
“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.)
“There is no such thing as “the Queen’s English.” The property has gone into the hands of a joint stock company and we own the bulk of the shares!”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)