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 something that Governments care for far more than human life, and that is the security of property, and so it is through property that we shall strike the enemy.... Be militant each in your own way.... I incite this meeting to rebellion.”
—Emmeline Pankhurst (1858–1928)
“In the Greek cities, it was reckoned profane, that any person should pretend a property in a work of art, which belonged to all who could behold it.”
—Ralph Waldo Emerson (1803–1882)
“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)