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 awareness of the all-surpassing importance of social groups is now general property in America.”
—Johan Huizinga (1872–1945)
“Open the doors of opportunity to talent and virtue and they will do themselves justice, and property will not be in bad hands.”
—Ralph Waldo Emerson (1803–1882)
“Thieves respect property. They merely wish the property to become their property that they may more perfectly respect it.”
—Gilbert Keith Chesterton (1874–1936)