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CIRCLES

CIRCLES. Everything you wanted to know and then some!!. C. Circle – set of all points _________ from a given point called the _____ of the circle. equidistant. C. center . Symbol:. Parts of a Circle. A secant line intersects the circle at exactly TWO points. SECANT sounds like second.

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CIRCLES

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  1. CIRCLES Everything you wanted to know and then some!!

  2. C Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol: Parts of a Circle

  3. A secant line intersects the circle at exactly TWO points. SECANT sounds like second Secant Line

  4. TANGENT: a LINE that intersects the circle exactly ONE time

  5. Name the term that best describes the line. Secant Radius Diameter Chord Tangent

  6. More Pythagorean Theorem type problems! Yeah!!  Point of Tangency If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

  7. 1. Solve for x A 12 B 9 a2 + b2 = c2 x 92 + 122 = x2 x = 15

  8. S Party hat problems! If two segments from the same exterior point are tangent to a circle, then they are congruent. R T

  9. 5. Solve for x C A B

  10. Central Angle : An Angle whose vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P To name: use 3 letters C To name: use 2 letters B APB is a Central Angle

  11. measure of an arc = measure of central angle m AB m ACB m AE A E 96 Q = 96° B C = 264° = 84°

  12. m DAB = Tell me the measure of the following arcs. 240 D A 140 260 m BCA = R 40 100 80 C B

  13. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INTERCEPTEDARC INSCRIBEDANGLE

  14. 160 80 To find the measure of an inscribed angle…

  15. What do we call this type of angle? What is the value of x? What do we call this type of angle? How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!! 120 x y

  16. J K Q S M 3. If m JK = 80, find mJMK. 40  4. If mMKS = 56, find m MS. 112  Examples

  17. Case I:Vertex is ON the circle ANGLE ARC ARC ANGLE

  18. Ex. 2 Find m1. 1 84° m1 = 42

  19. Case II:Vertex is inside the circle A ARC B ANGLE D ARC C Looks like a PLUS sign!

  20. Ex. 4 Find m1. 93° A B 1 D C 113° m1 = 103

  21. Case III:Vertex is outside the circle C ANGLE small ARC A D LARGE ARC B LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  22. Ex. 7 Find mAB. mAB = 16 A 27° 70° B

  23. Ex. 8 Find m1. 260° 1 m1 = 80

  24. Two chords intersect INSIDE the circle Type 1: a ab = cd d c b

  25. Ex: 1 Solve for x. 9 12 6 3 x = 3 x x 2 2 x = 8 x 3 6 2 x = 1

  26. Two secants intersect OUTSIDE the circle Type 2: E A B C D EA•EB = EC•ED

  27. Ex: 3 Solve for x. B 13 A 7 E 4 C x D (7 + 13) 7 140 = 16 + 4x (4 + x) = 4 124 = 4x x = 31

  28. Type 2 (with a twist): Secant and Tangent C B E A EA2= EB • EC

  29. Ex: 5 Solve for x. C B x 12 E 24 A (12 + x) 242 = 12 x = 36 576 = 144 + 12x

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