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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 C A B 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.

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Example A B D C

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Lines Intersecting On, Inside, or Outside a Circle On the circle Inside the circle Outside the circle Case 1 Case 2 Case 3 An inscribed angle

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Lines, or chords, intersecting inside a circle Theorem B A C D 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.

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Chords, intersecting inside a circle Example B A C D

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Lines Intersecting Outside a Circle Three scenarios! tangent-secant tangent-tangent secant-secant

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Tangent - Secant B A C

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Tangent - Tangent Q P R

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Secant - Secant B A D C

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Example B A C Find x:

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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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