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Over Lesson 10–5 5-Minute Check 1 A.yes B.no Determine whether BC is tangent to the given circle. ___ A.A B.B
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Over Lesson 10–5 5-Minute Check 2 A.yes B.no Determine whether QR is tangent to the given circle. ___ A.A B.B
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Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 3 12 Find x. Assume that segments that appear to be tangent are tangent.
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Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 4 Find x. Assume that segments that appear to be tangent are tangent.
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Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 5 SL and SK are tangent to the circle. Find x. ___ 5
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Then/Now Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle.
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Vocabulary secant—A line that intersects a circle in two points.
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Concept
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Example 1 Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer: x = 82
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Example 1 Use Intersecting Chords or Secants B. Find x. Theorem 10.12 Substitution Simplify. Step 1Find m VZW.
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Example 1 Use Intersecting Chords or Secants Step 2Find m WZX. WZX =180 – VZWDefinition of supplementary angles x =180 – 79Substitution x =101Simplify. Answer: x = 101
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C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Example 1 Use Intersecting Chords or Secants Subtract 25 from each side. Answer: x = 95
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A.A B.B C.C D.D Example 1 98 A. Find x.
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A.A B.B C.C D.D Example 1 95 B. Find x.
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A.A B.B C.C D.D Example 1 104 C. Find x.
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Concept
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Example 2 Use Intersecting Secants and Tangents A. Find m QPS. Theorem 10.13 Substitute and simplify. Answer: m QPS = 125
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B. Theorem 10.13 Example 2 Use Intersecting Secants and Tangents Substitution Multiply each side by 2. Answer:
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A.A B.B C.C D.D Example 2 112.5 A. Find m FGI.
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A.A B.B C.C D.D Example 2 162 B.
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Concept
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Example 3 Use Tangents and Secants that Intersect Outside a Circle A. Theorem 10.14 Substitution Multiply each side by 2.
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Example 3 Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1.
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Example 3 Use Tangents and Secants that Intersect Outside a Circle B. Theorem 10.14 Substitution Multiply each side by 2.
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Example 3 Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side.
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A.A B.B C.C D.D Example 3 23 A.
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A.A B.B C.C D.D Example 3 230 B.
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Example 4 Apply Properties of Intersecting Secants Theorem 10.14 Substitution
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Example 4 Apply Properties of Intersecting Secants Multiply each side by 2. Subtract 96 from each side. Multiply each side by –1.
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A.A B.B C.C D.D Example 4 40
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Concept
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