Download An inscribed quadrilateral is any four sided figure whose vertices all

An inscribed angle is an angle with its vertex "on" the circle, formed by two
intersecting chords. Its intercepted arc is the minor arc from A to C. The minor arc
has double the measure of the inscribed angle. For example, angle x would be 50°.
A central angle is an angle whose apex (vertex) is the center O of a circle and
whose legs (sides) are radii intersecting the circle in two distinct points A and B
thereby intercepting an arc between those two points whose angle is (by definition)
equal to that of the central angle itself. For example, angle x is 80°.
A circumscribed angle is an angle whose rays are tangent to the circle. The measure
of the angle is supplementary to the central angle formed by the perpendicular radii to
the tangents. If
, then
=50°.
An inscribed quadrilateral is any four sided figure whose vertices all lie on a
circle. (The sides are therefore chords in the circle!) The opposite angles of such
a quadrilateral are in fact supplementary angles. In other words, the sum of their
measures is 180 degrees.
The angle inscribed in a semicircle is always a right angle (90°). Therefore, the
triangle inscribed in a semicircle whose side is the diameter, must be a right
triangle.