9.4

-Define angles formed by secants and tangents of circles. -Develop and use theorems about measures of arcs intercepted by these angles
 * Objectives:**


 * Vocabulary:

Theory 1:** If a tangent and secant (or a chord) intersects on a circle at the point of tangency, then the measure of the angle formed is one-half the measure of its intercepted arc.


 * Theory 2:** the measure of an angle formed by two secants or chords that intersect in the interior of a circle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.


 * Theory 3:** The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference at the measure of the intercepted arcs.


 * Theory 4:** The meaasure of a secant-tangent angle with the vertex outside the circle is one-half the difference of the measures of the intercepted arcs.

(//The pictures link is to the original picture, I edited it.)//
 * Theory 5:** The measure of a tangent-tangent angle with the vertex outside the circle is one-half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180°