Section+9.4+swann

=Section 9.4=

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

Theorems:
then the measure of the angle formed is **half** the measure of its intercepted arc. the interior of the circle is **half** of the **sum** of the measures of the arcs intercepted by th angle and its vertical angle. of the circle is **half** the **difference** of the measures of the intercepted arcs.
 * If a tangent and a secant (or a chord) intersects on a circle at the point of tangency,
 * The measure of an angle formed by two secants or chords that intersect in
 * The measure of an angle formed by two secants that intersect in the exterior

Example: Find the measure of angle AQC. Two secants intersect the inside circle. The the theorem that deals with secants intersecting inside circles, the measure of angle AQC is half the sum of the two arcs. So, with arc AC being 30˚, and arc BD being 70˚, the sum being 100˚, and if you divide that in 1/2, angle is 50˚.