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10.1 : Chords and Arcs

10.1 : Chords and Arcs. Obj : _____________________ ___________________________. Parts of a Circle. Radius: segment from the center of the circle to a point on the circle Chord: segment whose endpoints lie on a circle Diameter: Chord that contains

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10.1 : Chords and Arcs

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  1. 10.1: Chords and Arcs Obj: _____________________ ___________________________

  2. Parts of a Circle • Radius: segment from the center of the circle to a point on the circle • Chord: segment whose endpoints lie on a circle • Diameter: Chord that contains the center of the circle

  3. More Parts Arc: an unbroken part of a circle Naming Arcs: Name the 2 endpoints and draw an arc on top

  4. Semicircle: an arc whose endpoints are endpoints of a diameter Naming Semicircles: Name an endpoint, another pt on arc, other endpt, with arc on tops

  5. Minor Arcs; Arc that is less than a semicircle Naming Minor Arcs: Name 2 endpts with arc on top

  6. Major Arc: More than a semicircle Naming major arcs: Name endpt, another pt, other endpt, with arc on top

  7. Practice • Name the following if P is the center • A) Radius • B) Diameter • C) Chord • D) Semicircle • E) Minor Arc • F) Major Arc

  8. Even More Parts • Central Angle: angle whose vertex is the center of the circle • Intercepted Arc: Arc whose endpts lie on the sides of the angle • Degree Measure of Arcs: Measure of the central angle

  9. M (2r). L = 360 9.1 Chords and Arcs Theorems, Postulates, & Definitions Arc Length: Where L= Arc Length M= Deg of central angle r = radius

  10. Example • Find the arc Length

  11. 9.1 Chords and Arcs Key Skills Find central angle measures. In circle M, find mAMB. Because 180 + 45 + mAMB = 360, mAMB = 135.

  12. In circle M, find mBC and the length of BC. = mBMC = 45, so length of mBC 45 mBC = (2)(20) = 15.71 meters. 360 TOC 9.1 Chords and Arcs Key Skills Find arc measures and lengths.

  13. 9.1 Chords and Arcs Theorems, Postulates, & Definitions Chords and Arcs Theorem: In a circle, or in congruent circles, the arcs of congruent chords are congruent. The Converse of the Chords and Arcs Theorem: In a circle, or in congruent circles, the chords of congruent arcs are congruent.

  14. Practice:

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