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Lesson 10.2

Lesson 10.2. Arcs and Chords. central angle. Arcs of Circles. Central Angle-angle whose vertex is the center of the circle. minor arc. Minor Arc. formed from a central angle less than 180 °. major arc. Major Arc. formed from a central angle that measures between 180 ° - 360 °.

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Lesson 10.2

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  1. Lesson 10.2 Arcs and Chords

  2. central angle Arcs of Circles • Central Angle-angle whose vertex is the center of the circle.

  3. minor arc Minor Arc • formed from a central angle less than 180°

  4. major arc Major Arc • formed from a central angle that measures between 180 ° - 360 °

  5. Semicircle • formed from an arc of 180 ° • Half circle! • Endpoints of an arc are endpoints of the diameter

  6. Naming Arcs • How do we name minor arcs, major arcs, and semicircles??

  7. Minor Arc: AB or BA Minor Arc • Named by the endpoints of the arc.

  8. Major Arc: ACB or BCA Could we name this major arc BAC? Major Arc • Named by the endpoints of the arc and one point in between the arc

  9. mABC = 180° Semicircle • Named by the endpoints of the diameter and one point in between the arc

  10. Example

  11. Measuring Arcs • A Circle measures 360 °

  12. m AB=95 ° 95° Measure of a Minor Arc • Measure of its central angle

  13. 95° mACB=360°– 95° = 265° Measure of a Major Arc • difference between 360° and measure of minor arc

  14. What is the measure of BD? m BD=100 ° Arc Addition Postulate • Measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

  15. Example for #1-10

  16. AB is congruent to DC since their arc measures are the same. Congruent Arcs • Two arcs of the same circle or congruent circles are congruent arcs if they have the same measure.

  17. Theorem 10.4 • Two minor arcs are congruent iff their corresponding chords are congruent. Chords are congruent

  18. Example 1Solve for x 2x X+40

  19. If DE = EF, then DG = GF Theorem 10.5 • If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

  20. m DC = 40º Example. Find DC.

  21. Since AB is perpendicular to CD, CD is the diameter. Theorem 10.6 • If one chord is a perpendicular bisector to another chord, then the first chord is a diameter.

  22. Example. Solve for x. x = 7

  23. Theorem 10.7 • Two chords are congruent iff they are equidistant from the center. Congruent Chords

  24. Example. Solve for x. x = 15

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