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# Other Angle Relationships - PowerPoint PPT Presentation

Other Angle Relationships. Section 10.6. Tangent-Chord Theorem. If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. . Example 1. Try This!. Example 2. Interior Intersection Theorem.

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## PowerPoint Slideshow about ' Other Angle Relationships' - eugene

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### Other Angle Relationships

Section 10.6

• If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

• If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

• If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

Diagrams for Exterior Intersection Theorem

• Find the value of x.

• Find the value of x.

• Find the value of x.

• Find the value of x.

• If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

• Find the value of x.

• Find the value of x.

• If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.

• If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment.

• Find the value of x.

• Find the value of x.

• Find the value of x.

• Find the value of x.