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Published byRachel Hollis Modified over 3 years ago

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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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Warm up X = 6 X = 5.4 X = 20.8 X = 5X = 10. A little extra information ♥The word tangent comes from the Latin word meaning to touch ♥The word secant comes.

Warm up X = 6 X = 5.4 X = 20.8 X = 5X = 10. A little extra information ♥The word tangent comes from the Latin word meaning to touch ♥The word secant comes.

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