9.4+(WiBr56)

__Theorem__ If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is 1/2 the measure of its intercepted arc.

__Theorem__ The measure of an angle formed by two secants or chords that intersect in the interior of a circle is the 1/2 of the sum of the measures of the arcs intercepted by the angle and its vertical angle.

__Theorem__ The measure of an angle formed by two secants that intersect in the exterior of a circle is 1/2 the difference of the measures of the intercepted arcs.

__Theorem__ The measure of a secant - tangent angle with its vertex outside the circle is 1/2 the difference of the measures of the intercepted angles.

__Theorem__ The measure of a tangent - tangent angle with its vertex outside the circle is 1/2 the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180 degrees.

__Example__ 70 degrees + 35 degrees /2 105 / 2 x = 52.5 degrees
 * Find angle APB**



For More Information http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_InteriorAngles.xml