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 charming landscape which I saw this morning is indubitably made up of some twenty or thirty farms. Miller owns this field, Locke that, and Manning the woodland beyond. But none of them owns the landscape. There is property in the horizon which no man has but he whose eye can integrate all parts, that is, the poet. This is the best part of these men’s farms, yet to this their warranty-deeds give no title.”
—Ralph Waldo Emerson (1803–1882)
“Communism is inequality, but not as property is. Property is exploitation of the weak by the strong. Communism is exploitation of the strong by the weak.”
—Pierre-Joseph Proudhon (1809–1865)
“There is something that Governments care for far more than human life, and that is the security of property, and so it is through property that we shall strike the enemy.... Be militant each in your own way.... I incite this meeting to rebellion.”
—Emmeline Pankhurst (1858–1928)