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

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

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.

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.

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

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.

Vocabulary secant—A line that intersects a circle in two points.

Concept

Example 1 Use Intersecting Chords or Secants A. Find x. Theorem Substitution Simplify. Answer: x = 82

Example 1 Use Intersecting Chords or Secants B. Find x. Theorem Substitution Simplify. Step 1Find m  VZW.

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

C. Find x. Theorem Substitution Multiply each side by 2. Example 1 Use Intersecting Chords or Secants Subtract 25 from each side. Answer: x = 95

A.A B.B C.C D.D Example 1 98 A. Find x.

A.A B.B C.C D.D Example 1 95 B. Find x.

A.A B.B C.C D.D Example C. Find x.

Concept

Example 2 Use Intersecting Secants and Tangents A. Find m  QPS. Theorem Substitute and simplify. Answer: m  QPS = 125

B. Theorem Example 2 Use Intersecting Secants and Tangents Substitution Multiply each side by 2. Answer:

A.A B.B C.C D.D Example A. Find m  FGI.

A.A B.B C.C D.D Example B.

Concept

Example 3 Use Tangents and Secants that Intersect Outside a Circle A. Theorem Substitution Multiply each side by 2.

Example 3 Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1.

Example 3 Use Tangents and Secants that Intersect Outside a Circle B. Theorem Substitution Multiply each side by 2.

Example 3 Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side.

A.A B.B C.C D.D Example 3 23 A.

A.A B.B C.C D.D Example B.

Example 4 Apply Properties of Intersecting Secants Theorem Substitution

Example 4 Apply Properties of Intersecting Secants Multiply each side by 2. Subtract 96 from each side. Multiply each side by –1.

A.A B.B C.C D.D Example 4 40

Concept