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

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

3. Secant Line A secant line intersects the circle at exactly TWO points.

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. 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!!

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

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

9. A C B

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

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

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

13. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INSCRIBED ANGLE INTERCEPTED ARC

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

15. 120 x What do we call this type of angle? What is the value of x? y 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!!

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

17. 72  If two inscribed angles intercept the same arc, then they are congruent.

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

19. Ex. 2 Find m1. 84 ° 1 m  1 = 42 

20. Case II: Vertex is inside the circle A B C D ANGLE ARC

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

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

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

24. 1 Ex. 8 Find m1. 260° m  1 = 80 

25. a b c d ab = cd

26. 9 2 6 x x = 3 3 2 1212 x x = 8 3 26 x x = 1 Ex: 1 Solve for x.

27. EAB C D EA EB = EC ED

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

29. E A B C EA 2 = EB EC

30. E A B C 24 12 x 24 2 =12 (12 + x) 576 = 144 + 12x x = 36 Ex: 5 Solve for x.