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:
“It is clearly better that property should be private, but the use of it common; and the special business of the legislator is to create in men this benevolent disposition.”
—Aristotle (384–322 B.C.)
“By avarice and selfishness, and a groveling habit, from which none of us is free, of regarding the soil as property, or the means of acquiring property chiefly, the landscape is deformed, husbandry is degraded with us, and the farmer leads the meanest of lives. He knows Nature but as a robber.”
—Henry David Thoreau (1817–1862)
“It is as if being was to be observed,
As if, among the possible purposes
Of what one sees, the purpose that comes first,
The surface, is the purpose to be seen,
The property of the moon, what it evokes.”
—Wallace Stevens (1879–1955)