1. Warm – up Session 48

2. EOCT Review

3. Homework Review

4. CCGPS Geometry 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) Same center but different radii

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

11. 2 points of intersection

12. Common Tangents Internal

13. Common Tangents External

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

15. a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2

16. a 2 + b 2 = c 2 RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2

17. No a 2 + b 2 = c 2 ?

18. r 2 + 24 2 = (r + 16) 2 r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r

19. 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. a)What is the radius? b) How far is your ball from the cup at the center? x = 60 ft. x = 68 ft.

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

21. R S T

22. R S T

23. A C B

24. A C E B D P

25. T S Q P N R