Page 2: Advanced Angle Relationships in Circles
This page delves into more complex angle relationships in circles, including chord-chord angles, tangent-secant angles, tangent-tangent angles, and secant-secant angles.
Definition: A chord-chord angle is formed by two chords intersecting inside a circle.
Definition: A tangent-secant angle is formed by a tangent and a secant intersecting at a point outside the circle.
Definition: A tangent-tangent angle is formed by two tangents intersecting at a point outside the circle.
Definition: A secant-secant angle is formed by two secants intersecting at a point outside the circle.
The page provides formulas for calculating these angles:
Highlight: For a chord-chord angle, the measure of the angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Highlight: For angles formed outside the circle tangent−secant,tangent−tangent,andsecant−secant, the measure of the angle is half the difference of the intercepted arcs.
Examples are given to demonstrate how to apply these formulas in problem-solving scenarios.
Example: One problem asks students to find the measure of angle RTS given that one intercepted arc measures 100° and another measures 160°.
