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:
“No man acquires property without acquiring with it a little arithmetic, also.”
—Ralph Waldo Emerson (1803–1882)
“Crimes increase as education, opportunity, and property decrease. Whatever spreads ignorance, poverty and, discontent causes crime.... Criminals have their own responsibility, their own share of guilt, but they are merely the hand.... Whoever interferes with equal rights and equal opportunities is in some ... real degree, responsible for the crimes committed in the community.”
—Rutherford Birchard Hayes (1822–1893)
“As a man is said to have a right to his property, he may equally be said to have a property in his rights.”
—James Madison (1751–1836)