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ARCs and chords

ARCs and chords. Geometry CP2 (Holt 12-2) K.Santos. Central Angle. Central angle ----an angle—vertex----center A B O < AOB is a central angle. Chords and Arcs. Chord —endpoints are on the circle A B

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ARCs and chords

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  1. ARCs and chords Geometry CP2 (Holt 12-2) K.Santos

  2. Central Angle Central angle----an angle—vertex----center A B O < AOB is a central angle

  3. Chords and Arcs Chord—endpoints are on the circle A B Arc—is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them (curved part of circle)

  4. Arcs and their measures Minor arc small arc (smaller than half circle)---between 0-180 Measure = central angle Name with two letter Major arc--- big arc (bigger than half circle)---between 180-360 Measure = 360- minor arc name with 3 letters Semicircle---arc is half the circle Measure = 180 name with 3 letters

  5. Arcs M N O P Minor Arcs:Major Arcs:Semicircle: If m<MON = 50 find m, mand m m = 50 m = 180-50 = 130 m= 360 – 50 = 310

  6. Adjacent Arcs Adjacent Arcs—arcs of the same circle next to each other (share endpoint) R S O U T and and

  7. Arc Addition Postulate 12-2-1 The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. A B C Add 2 little arcs together to get big arc m = m + m

  8. Example Find m and m. M Y 40 56 D W X m = m + m m = 40 + 56 m = 96 m= m + m m= 56 + 180 m= 236

  9. Theorem 12-2-2 Within a circle or in congruent circles: Congruent central angles Congruent chords Congruent arcs

  10. Example Find each measure. V (9x – 11) . Find m. W T (7x + 11) S 9x – 11= 7x + 11 (congruent arcs---congruent chords) 2x -11 = 11 2x = 22 x = 11 WS = 7x + 11 WS = 77 + 11 = 88

  11. Theorem 12-2-3 (12-2-4) Radius (or diameter) is perpendicular to a chord----- bisects the chord and its arc. D A B C F Given: is a diameter and is perpendicular to Then: is bisected ( is bisected (

  12. Example Find the value of x. 5 x 5 6 Chords are equidistant from the center so the chords are congruent Bottom chord is 2(6) = 12, so the chord on the right is also 12. Thus, x = 12

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