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Warm – up Session 48

Warm – up Session 48. EOCT Review. Question of the Day. Homework Review. CCGPS Geometry Day 48 (3-28-14). UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question:

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Warm – up Session 48

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  1. Warm – up Session 48

  2. EOCT Review Question of the Day

  3. Homework Review

  4. CCGPS GeometryDay 48 (3-28-14) UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: What other angle relationships do we know for circles? Standard: MMC9-12.G.C.2

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

  6. Point of Tangency

  7. Two circles can intersect… • in two points • one point • or no points

  8. No points of intersection (different center)

  9. No points of intersection (same center) Concentric Circles Same center but different radii

  10. 1 point of intersection(Tangent Circles) Externally Tangent Internally Tangent

  11. 2 points of intersection

  12. 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.

  13. 1. Find x A 12 B 9 a2 + b2 = c2 x 92 + 122 = x2 x = 15

  14. 2. Find RQ a2 + b2 = c2 122 + (QR)2 = (8+12)2 P 122 + (QR)2 = 202 12 8 RQ = 16 R Q

  15. 3. Is BC tangent to the circle? a2 + b2 = c2 ? No A 32 C 16 24 B

  16. r2 + 242 = (r + 16)2 4. Find the radius. r2 + 576= r2 + 32r + 256 320= 32r 16 r = 10 A C 24 B

  17. A green on a golf course is in the shape of a circle. Your golf ball is 8 feet from the edge of the green and 32 feet from a point of tangency on the green. • What is the radius? • b) How far is your ball from the cup at the center? x = 60 ft. x = 68 ft.

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

  19. 6. Find x R S T

  20. 7. Find x R S T

  21. 8. Find x C A B

  22. 9. Find x. B A C P D E

  23. 10. Find NP N T S P R Q

  24. CW Workbook Page 199 #18-33

  25. HW Worksheet

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