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:
“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)
“No man is by nature the property of another. The defendant is, therefore, by nature free.”
—Samuel Johnson (1709–1784)
“I have no concern with any economic criticisms of the communist system; I cannot enquire into whether the abolition of private property is expedient or advantageous. But I am able to recognize that the psychological premises on which the system is based are an untenable illusion. In abolishing private property we deprive the human love of aggression of one of its instruments ... but we have in no way altered the differences in power and influence which are misused by aggressiveness.”
—Sigmund Freud (1856–1939)