Page 2: On-Circle and Exterior Intersections

This page delves into two crucial scenarios: intersections occurring on the circle and exterior intersections. It presents the theorems for calculating angles when a secant and a tangent intersect in the exterior of a circle and when lines meet at the circle's circumference.

Definition: For exterior intersections, the angle measure equals half the difference of the intercepted arcs.

Highlight: The page presents three distinct cases for exterior intersections: two secants, secant and tangent, and two tangents.

Example: Problem 7 shows that for an angle on the circle, mZDEG = 308°/2 = 154°, demonstrating the application of the on-circle intersection formula.

Vocabulary: Point of tangency - the point where a tangent line touches the circle's circumference.

Page 3: Practice Problems and Applications

The final page provides extensive practice with various angle calculations involving angles formed by chords, tangents, and secants. It presents complex problems that require applying the theorems learned in previous pages.

Example: Problem 13 demonstrates solving for an unknown arc measure: 40° = 2(x-75°), leading to x = 155°.

Highlight: The problems progress in complexity, incorporating all three types of intersections covered in the lesson.

Vocabulary: Arc measure - the degree measurement of a portion of the circle's circumference.