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 English language is nobody’s special property. It is the property of the imagination: it is the property of the language itself.”
—Derek Walcott (b. 1930)
“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)
“Strange and predatory and truly dangerous, car thieves and muggers—they seem to jeopardize all our cherished concepts, even our self-esteem, our property rights, our powers of love, our laws and pleasures. The only relationship we seem to have with them is scorn or bewilderment, but they belong somewhere on the dark prairies of a country that is in the throes of self-discovery.”
—John Cheever (1912–1982)