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:
“For wisdom is the property of the dead,
A something incompatible with life; and power,
Like everything that has the stain of blood,
A property of the living; but no stain
Can come upon the visage of the moon
When it has looked in glory from a cloud.”
—William Butler Yeats (1865–1939)
“A lawyer’s dream of Heaven: Every man reclaimed his own property at the resurrection, and each tried to recover it from all his forefathers.”
—Samuel Butler (1835–1902)
“General education is the best preventive of the evils now most dreaded. In the civilized countries of the world, the question is how to distribute most generally and equally the property of the world. As a rule, where education is most general the distribution of property is most general.... As knowledge spreads, wealth spreads. To diffuse knowledge is to diffuse wealth. To give all an equal chance to acquire knowledge is the best and surest way to give all an equal chance to acquire property.”
—Rutherford Birchard Hayes (1822–1893)