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**Other Angle Relationships in Circles Section 10.4**

Goal: - To solve problems using angles formed by tangents, chords and lines that intersect a circle.

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Theorem 10.12 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. C B A

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Example C B A D

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**Lines Intersecting On, Inside, or Outside a Circle**

On the circle Inside the circle Outside the circle Case Case Case 3 An inscribed angle

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**Lines, or chords, intersecting inside a circle Theorem 10.13**

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

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**Chords, intersecting inside a circle Example**

B

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**Lines Intersecting Outside a Circle Three scenarios!**

tangent-secant tangent-tangent secant-secant

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Tangent - Secant Tangent-Secant A B C

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Tangent - Tangent Tangent-Tangent P Q R

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Secant - Secant Secant-Secant A D B C

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Example Find x: A B C

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Example Find x:

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Example Find x:

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Example Find x:

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Bellwork One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x.

Bellwork One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle Solve for x 2x.

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