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Unit 3

Unit 3. Circles & Lines. Section 1. Key Terms. Write down everything you know about circles!. Chord. Line segment that connects two points on a circle Chords equidistant from the center are congruent. Diameter & Radius. Diameter: Chord passing through the center of the circle

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Unit 3

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  1. Unit 3 Circles & Lines

  2. Section 1 Key Terms

  3. Write down everything you know about circles!

  4. Chord • Line segment that connects two points on a circle • Chords equidistant from the center are congruent

  5. Diameter & Radius • Diameter: Chord passing through the center of the circle • Radius: Line segment from the center to the circumference (outside)

  6. Tangent • Line that touches a circle at exactly one point

  7. Secant • Line that passes through a circle at two points • What’s the difference between a chord, a tangent, and a secant?

  8. Arc • Curve that makes up the circle • Minor Arc: less than 180° • Major Arc: greater than 180° • Semicircle: exactly 180° (half the circle)

  9. Central Angle • Angle whose vertex is on the center of the circle • Measure of a central angle is equal to the measure of the intercepted arc

  10. Example 2

  11. Wrap Up • Exit Slip • Unit 3 Homework Packet

  12. Section 2 Chords

  13. Chords & Arcs • Chords intercepting congruent arcs are congruent • Example: Find the measure of arc AC if arc BA = 150°, and arc BA is congruent to arc CB.

  14. Distance from a Chord to the Center • Example: What is the length of BD? • Hint: What shape do you see in this diagram?

  15. Section 3 Tangents

  16. Tangents • How many tangents can you draw that touch both circles at exactly one point?

  17. Tangents are Perpendicular to the Radius they Intersect • Find the radius. 15 17

  18. Wrap Up • Exit Slip • Homework Packet

  19. Section 4 Arc-Angle Relationships

  20. Inscribed Angle • Angle whose vertex is on the circle • Inscribed angle = Intercepted arc • Example: The measure of arc AC is 80°. Find the measure of AOC and ABC.

  21. Angles Inside the Circle • Angle = ½ (Arc 1 + Arc 2) • Arc BD = 60° and arc AC = 100°. Find the measure of angle AEC. A E D C B

  22. Angles Outside the Circle • Angle = ½ (Arc 1 – Arc 2) • Chord LP is congruent to chord NM. Arc LP measures 130°. Arc LN is three times the measure of arc PM. Find the measure of angle PQM. L P Q M N

  23. Example

  24. Wrap Up • Exit Slip • Homework Packet

  25. Section 5 Segment Product Theorem

  26. Arcs Between Parallel Lines are Congruent • Name the two congruent arcs. A B D C

  27. Segment Product Theorem #1 • LINES, not angles or arcs! • Chord-Chord: AE × EB = CE × ED • Example: Find x. A 9 E 6 3 D C x B

  28. Segment Product Theorem #2 • Tangent-Tangent: CD = AD • “Hat Rule” • Can you prove this?

  29. Segment Product Theorem #3 • Tangent-Secant: PA2 = PB × PC • Example: If PB is 2 inches and BC is 16 inches, find PA.

  30. Segment Product Theorem #4 • Secant-Secant: BE × AE = DE × CE • Example: If AB = 5, CD = 10, and DE = 12, what is the length of BE?

  31. Wrap Up • Exit Slip • Homework Packet Due Friday • Unit 3 Test Friday

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