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:
“To throw obstacles in the way of a complete education is like putting out the eyes; to deny the rights of property is like cutting off the hands. To refuse political equality is like robbing the ostracized of all self-respect, of credit in the market place, of recompense in the world of work, of a voice in choosing those who make and administer the law, a choice in the jury before whom they are tried, and in the judge who decides their punishment.”
—Elizabeth Cady Stanton (1815–1902)
“Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)
“Strange and predatory and truly dangerous, car thieves and muggers—they seem to jeopardize all our cherished concepts, even our self-esteem, our property rights, our powers of love, our laws and pleasures. The only relationship we seem to have with them is scorn or bewilderment, but they belong somewhere on the dark prairies of a country that is in the throes of self-discovery.”
—John Cheever (1912–1982)