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:
“I would gladly chastise those who represent things as different from what they are. Those who steal property or make counterfeit money are punished, and those ought to be still more severely dealt with who steal away or falsify the good name of a prince.”
—Elizabeth I (1533–1603)
“Those whom the gods chose as their property must not consort with mortals.”
—Franz Grillparzer (1791–1872)
“Never let the estate decrease in your hands. It is only by such resolutions as that that English noblemen and English gentlemen can preserve their country. I cannot bear to see property changing hands.”
—Anthony Trollope (1815–1882)