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# 11-5 - PowerPoint PPT Presentation

11-5. Angle Relationships in Circles. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. chords: AE , CD secant: AE tangent: AB. Warm Up 1. Identify each line or segment that intersects  F . Find each measure. 2. m  NMP 3. m  NLP. 110°. 55°. Objectives.

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Presentation Transcript

Angle Relationships in Circles

Warm Up

Lesson Presentation

Lesson Quiz

Holt Geometry

chords:AE,CD

secant: AE

tangent: AB

Warm Up

1.Identify each line or segment that intersects F.

Find each measure.

2. mNMP

3. mNLP

110°

55°

Find the measures of angles formed by lines that intersect circles.

Use angle measures to solve problems.

Tangent-Chord Angles

Find each measure.

mEFH

= 65°

Tangent-Chord Angles

Find each measure.

a Circle

Find each measure.

mAEB

= 126

Check It Out! Example 2b

Find each angle measure.

mRNM

mRNM = 180° – MNQ

mRNM = 180° – 158° = 22°

Tangents and Secants

Find the value of x.

= 40

= 63

In the company logo shown, = 108°, and = 12°. What is mFKH?

Example 4: Design Application

Two of the six muscles that control eye movement are attached to the eyeball and intersect behind the eye. If mAEB = 225, what is mACB?

Check It Out! Example 4

Find attached to the eyeball and intersect behind the eye. If m

Step 1 Find

U

V

Substitute 180 – 113 for mXVY and 68 for mWZ

Example 5: Finding Arc Measures

If a tangent and a secant intersect on a  at the pt. of tangency, then the measure of the  formed is half the measure of its intercepted arc.

Multiply both sides by 2.

Subtract 68 from both sides.

Step 2 attached to the eyeball and intersect behind the eye. If m Find

U

V

Example 5 Continued

Thm. 11-5-3

Substitute the given values.

Multiply both sides by 2.