SECTION+9.4+ANGLES+FOMRED+BY+SECANTS+AND+TANGENTS

Objectives: 1. Define angles formed by secants and tangents of circles 2. Develop and use theorems about measures of arcs intercepted by these angles


 * __DEFINITIONS AND BLUE BOXES!!__**

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