Geometry Unit 9 9 7 Lengths of Segments

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Geometry Unit 9 9 -7: Lengths of Segments in Circles

Geometry Unit 9 9 -7: Lengths of Segments in Circles

Warm-up Identify the type of line, arc or angle that is made based off

Warm-up Identify the type of line, arc or angle that is made based off the picture and the notation given. Major Arc Diameter Chord Tangent Secant Minor Arc Radius Central Angle Semicircle Inscribed Angle G

Segment Lengths in Circles • Content Objective: Students will be able to identify segments

Segment Lengths in Circles • Content Objective: Students will be able to identify segments created by chords, secants, and tangents inside and outside of circles. • Language Objective: Students will be able to solve for the measures of segments created by chords, secants, and tangents by using equations.

Segment Lengths in Circles • D A P C B

Segment Lengths in Circles • D A P C B

Segment Lengths in Circles • Theorem 9 -11: When two chords intersect inside a

Segment Lengths in Circles • Theorem 9 -11: When two chords intersect inside a circle, the of product the segments of one chord equals the product of the segments of the other chord. D A P C B

Segment Lengths in Circles • Theorem 9 -12: When two secant segments are drawn

Segment Lengths in Circles • Theorem 9 -12: When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.

Segment Lengths in Circles • Theorem 9 -13: When a secant segment and a

Segment Lengths in Circles • Theorem 9 -13: When a secant segment and a tangent are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.

Examples Chords, Secants, and Tangents are shown. Find the value of x. 1. )

Examples Chords, Secants, and Tangents are shown. Find the value of x. 1. ) 6 8

Examples Chords, Secants, and Tangents are shown. Find the value of x. 2. )

Examples Chords, Secants, and Tangents are shown. Find the value of x. 2. ) 4

Examples Chords, Secants, and Tangents are shown. Find the value of x. 3. )

Examples Chords, Secants, and Tangents are shown. Find the value of x. 3. )

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 1.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 1. ) 4 5 8

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 2.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 2. ) 9 16

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 3.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 3. ) 4 3

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 4.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 4. ) 5 3

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 5.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 5. ) 4 3 5

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 6.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 6. ) O 3 3

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 7.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 7. ) 6 5 4

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 8.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 8. ) x 8

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 9.

Group Practice Chords, Secants, and Tangents are shown. Find the value of x. 9. ) 10

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