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Circles!

Circles!. Arcs & Angles, Measurement. Arcs & Angles. Circle Vocabulary. Major Arc: Arc greater than 180 ⁰. Minor Arc: Arc less than 180⁰. Tangent: Line that intersects the circle at 1 point. Secant: Line that intersects the circle at 2 point.

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Circles!

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  1. Circles! Arcs & Angles, Measurement

  2. Arcs & Angles Circle Vocabulary Major Arc: Arc greater than 180⁰. Minor Arc: Arc less than 180⁰. Tangent: Line that intersects the circle at 1 point. Secant: Line that intersects the circle at 2 point. Chord: Segment whose endpoints are on the circle. Central Angle: Angle whose vertex is at the center. Inscribed Angle: Angle whose vertex is on the circle. DBA DA D AE DB C A DA E <BCA B <BDA

  3. Arcs & Angles Find the Magic Number! m<1 + m<2 + m<3 = ? D 1 mDA + mAB + mBD = ? C 2 A Sum of the Angles = ? Sum of the Arcs 3 B

  4. Outside Angle C 1 Use the Magic Number! ½ (big arc – small arc) = angle D B D C A E A B A 1 1 B C D

  5. Inside Angle Use the Magic Number! ½ arc = inscribed angle ½ (arc + arc) = angle A D B 1 C 1 B C A D

  6. Angles Both Outside & Inside Use the Magic Number! D ½ mDBA = m<2 1 C A ½ mDA = m<1 2 E B

  7. Right Angles & Circles mDAB = ? 180⁰ E m<1 = ? 90⁰ D ? radius. DC is a 1 ? tangent. DE is a A C The tangent is perpendicular to the radius. B

  8. Right Angles & Circles Prove DE ~ EA EACD is a kite! E Given ED , EA are tangent to C at D, A respectively. 1 If ED , EA are tangent, then <EDC and <EAC are right angles. D EC~ EC by the reflexive property. DC~ AC because they are radii. A ΔEDC ~ ΔEAC by HL (hyp-leg). C DE ~ EA by CPCTC B

  9. Angles & Circles Prove <1 ~ <2 Given DB ~ EA Remember <1 & <2 are NOT vertical! E D C 2 1 A B

  10. Angles & Circles Prove <1 ~ <2 Given DB ~ EA Remember <1 & <2 are NOT vertical! E D C 2 1 A B

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