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:
“A few days later the younger son gathered all he had and traveled to a distant country, and there he squandered his property in dissolute living.”
—Bible: New Testament, Luke 15:13.
“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)
“If property had simply pleasures, we could stand it; but its duties make it unbearable. In the interest of the rich we must get rid of it.”
—Oscar Wilde (1854–1900)