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:
“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)
“No man is by nature the property of another. The defendant is, therefore, by nature free.”
—Samuel Johnson (1709–1784)
“The second property of your excellent sherris is the warming
of the blood.”
—William Shakespeare (1564–1616)