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Warm-up

Name a segment tangent to circle A. What is the If BD = 36, find BC. If AC = 10 and BD = 24, find AB. If AD = 7 and BD = 24, find BE. Warm-up. D. B. E. A. C. Unit Question: What happens when line segments intersect a circle?. Today’s Question:

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Warm-up

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  1. Name a segment tangent to circle A. • What is the • If BD = 36, find BC. • If AC = 10 and BD = 24, find AB. • If AD = 7 and BD = 24, find BE. Warm-up D B E A C

  2. Unit Question:What happens when line segments intersect a circle? Today’s Question: How do you find the measure of angles formed by secant and tangent lines?

  3. Secant Anglesand Secant – Tangent Angles

  4. measure of an arc = measure of central angle m AB m ACB m AE A E 97 Q = 97° B C = 263° = 83°

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

  6. A secant line intersects the circle at exactly two points. SECANT sounds like second

  7. Ex. 1 Find m1. A B 1 124° C m<1 = 620

  8. Ex. 2 Find m1. 1 84° m<1 = 420

  9. Remember, a straight angle is 180 degrees!

  10. 108° Ex. 3 Find m1. 1 m<1 = 1260

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

  12. Ex. 4 Find m1. 93° A B 1 D C 113° m<1 = 1030

  13. Ex. 5 Find mQT. mQT = 1000 N Q 840 920 M T

  14. 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

  15. Ex. 6 Find m1. 1 15° A D 65° B m<1 = 250

  16. Ex. 7 Find mAB. m AB = 160 A 27° 70° B

  17. Ex. 8 Find m1. 240° 1 m<1 = 600

  18. pg 214 #1-15

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