Other angle relationships
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Other Angle Relationships PowerPoint PPT Presentation


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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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Other Angle Relationships

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Other angle relationships

Other Angle Relationships

Section 10.6


Tangent chord theorem

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

Example 1


Try this

Try This!


Example 2

Example 2


Interior intersection theorem

Interior Intersection Theorem

  • 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.


Exterior intersection theorem

Exterior Intersection Theorem

  • 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

Diagrams for Exterior Intersection Theorem


Example 3

Example 3

  • Find the value of x.


Try this1

Try This!

  • Find the value of x.


Example 4

Example 4

  • Find the value of x.


Example 5

Example 5

  • Find the value of x.


Chord product theorem

Chord Product Theorem

  • 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.


Example 11

Example 1

  • Find the value of x.


Try this2

Try This!

  • Find the value of x.


Secant secant theorem

Secant-Secant Theorem

  • 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.


Secant tangent theorem

Secant-Tangent Theorem

  • 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.


Example 21

Example 2

  • Find the value of x.


Try this3

Try This!

  • Find the value of x.


Example 31

Example 3

  • Find the value of x.


Try this4

Try This!

  • Find the value of x.


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