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Date:. Sec 10-2 Concept: Arcs and Chords Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g. DE. DBE. BD. Vocabulary:. Minor Arc ________ Major Arc _______ Central Angle _______ Semicircle __________. <DPE. Find Each Arc: CD _________

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  1. Date: Sec 10-2 Concept: Arcs and Chords Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g.

  2. DE DBE BD Vocabulary: • Minor Arc ________ • Major Arc _______ • Central Angle _______ • Semicircle __________ <DPE

  3. Find Each Arc: • CD_________ • CDB ________ • BCD _________ Measure of Minor Arc = Measure of Central Angle 148 328 180

  4. Find Each Arc: • BD_________ • BED ________ • BE _________ Measure of Minor Arc = Measure of Central Angle 142 218 118 118

  5. AB  BC IFF AB BC Thm 10-4: In the same or congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.

  6. X+20 3x mDC = x+20 =10+20 =30 Example: Find mDC given AD = 3x, DC = x+20 • 3x= x+20 • -x -x • 2x=20 • 2 • X=10

  7. IF PG DF, Then DE  EF and DG  GF Thm 10-5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc

  8. AB  CD IFF EG  EF Thm 10-7: In the same or in congruent circles 2 chords are congruent IFF they are equidistant from the center.

  9. 6 6 6 6 Example: AB =12, DE =12 , CE = 7, Find CG Since CG is  AB, AG  GB Also, CF is  DE, so, DF  FE Also, if AB = DE, then GC=CF Use pyth. Thm to find x, that will also be CG. X2+62 = 72 X2+36 = 49 -36 -36 X2= 13 X=3.6

  10. Proof:

  11. Date: Sec 10-3 Concept: Inscribed Angles Objective: Given an inscribed angle, find arc measures as measured by s.g.

  12. Inscribed Angle: An angle whose vertex is on a circle and whose sides contain chords of the circle. Intercepted Arc Inscribed Angle

  13. 80 x Example: Find the measure of the angle Measure of Inscribed Angle = ½ the intercepted Arc X = ½ the arc X=1/2(80) X=40

  14. x 60 Find the measure of the Arc Measure of Inscribed Angle = ½ the intercepted Arc 60 = ½ x ½ ½ X=120

  15. B 70 B A C C A D mADC = ______ mAC = _______ Example: Find the measure of each arc or angle 180 140

  16. B 72 C A Find the measure of <BCA 36 m<BCA = ______

  17. B 44 A C D Find m<C M<C = 44 88

  18. Example:

  19. Proof:

  20. Today’s work

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