Click+here+for+9.4

=9.4=

Objectives
Define angles formed by secants and tangents or circles Develop and use theorems about measures of arcs intercepted by these angles In this section we will learn about three different case...

Case 1*Vertex is on the circle
A.Tangent and a seacant B.Two secants ex.for Case 1 A ex.for Case 2B

Case 2*Vertex is inside the circle
Two secants ex.

Case 3*Vertex is outside the circle
A.Two tangents B.Two Secants C.Secant and Tangent ex.for Case 3 A.

ex.for Case 3 B Ex.For Case 3 C

=Theorems\= For each case there is a different theorem to find the measures of the arcs...for case one the theorem is.... If a tangent and a secant intersect on a circle at the point of tangancy then the measure of the angle formed is half the measure of its intercepted arc(same was in 9.3 with the inscribed angle theorem) For Case two the theorem is... The measure of an angle formed by two secants or chords that intersect in the interior of a circle is half the sum of the measures of the arcs intercepted by the angle and its vertical angles....like this .And the theorem for Case three is... The measure of an angle formed by two secants that intersect in the exterior of a cicle is half the difference of the measures of the intercepted arcs...like this... Other theorems to know--- The measure of a secant-tangent angle with its vertex outside the circle is 1/2 the difference of the measures of the interscepted arcs and The measures of a tangent-tangent angle with its 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* Click here for 9.5