Section 10.4 – Other Angle Relationships in Circles Chapter 10 - Circles Section 10.4 – Other Angle Relationships in Circles

Unit Goals Use angles formed by tangents and chords to solve problems.

What Is the Measure of the Arc and Angle?

Theorem 10.12 If a tangent and chord intersect at a point on the circle, then the measure of each angle formed is ½ of the measure of its intercepted arc.

Example Find the measure of the indicated arc or angle: 140º

Example Find the value of x:

Theorem 10.13 If two chords intersect at a point in a circle, then the measure of each angle formed is ½ the sum of the measures of the intercepted arcs.

Example Find the measure of the indicated angle: 20º 70º

Example Find the measure of the indicated angle: 90º 150º

Theorem 10.14 If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle is ½ the difference of the intercepted arcs.

Example Find the measure of the indicated angle: 94º 50º

Example Find the measure of the indicated angle: 130º 230º

Example Find the measure of the indicated angle: 190º 110º