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:
“The diversity in the faculties of men, from which the rights of property originate, is not less an insuperable obstacle to a uniformity of interests. The protection of these faculties is the first object of government.”
—James Madison (1751–1836)
“I would gladly chastise those who represent things as different from what they are. Those who steal property or make counterfeit money are punished, and those ought to be still more severely dealt with who steal away or falsify the good name of a prince.”
—Elizabeth I (1533–1603)
“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)