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:
“We do not deride the fears of prospering white America. A nation of violence and private property has every reason to dread the violated and the deprived.”
—June Jordan (b. 1939)
“It is a well-settled principle of the international code that where one nation owes another a liquidated debt which it refuses or neglects to pay the aggrieved party may seize on the property belonging to the other, its citizens or subjects, sufficient to pay the debt without giving just cause of war.”
—Andrew Jackson (1767–1845)
“You and I ... are convinced of the fact that if our Government in Washington and in a majority of the States should revert to the control of those who frankly put property ahead of human beings instead of working for human beings under a system of government which recognizes property, the nation as a whole would again be in a bad situation.”
—Franklin D. Roosevelt (1882–1945)