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Understanding Tangents and Angles Related to a Circle

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Explore the crucial concepts of circle geometry, focusing on tangents, angles, and their relationships. This session delves into various cases such as vertices located on the circle, inside the circle, and outside the circle, with examples that illustrate how to find unknown lengths and angles. Whether you're calculating BC from BD, determining AB from AC and BD, or finding BE based on AD and BD, this session provides a comprehensive warm-up to sharpen your skills in circle theorems. Perfect for reinforcing your understanding of geometry!

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Understanding Tangents and Angles Related to a Circle

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Presentation Transcript

  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. Session 25 Warm-up D B E A C

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

  3. Ex. 1 Find m1. A B 1 124° C m1= 62 °

  4. Ex. 2 Find m1. 1 84° m 1 = 42°

  5. 108° Ex. 3 Find m1. 1 m1= 126°

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

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

  8. Ex. 5 Find mQT. mQT = 100° N Q 84° 92° M T

  9. 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

  10. Ex. 6 Find m1. 1 15° A D 65° B m  1 = 25°

  11. Ex. 7 Find mAB. mQT = 16° A 27° 70° B

  12. Ex. 8 Find m1. 260° 1 m  1 = 80°

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