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:
“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)
“Crimes increase as education, opportunity, and property decrease. Whatever spreads ignorance, poverty and, discontent causes crime.... Criminals have their own responsibility, their own share of guilt, but they are merely the hand.... Whoever interferes with equal rights and equal opportunities is in some ... real degree, responsible for the crimes committed in the community.”
—Rutherford Birchard Hayes (1822–1893)
“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)