2. Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How are central angles different from inscribed angles? Standard: MM2G3.b

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

4. CHORD: A segment whose endpoints are on the circle

5. Diameter P DIAMETER: Distance across the circle through its center Also known as the longest chord.

6. P RADIUS: Distance from the center to point on circle Radius

7. D = r = ? r = D =

8. Use  P to determine whether each statement is true or false. P Q R T S

9. Secant Line: intersects the circle at exactly TWO points

10. a LINE that intersects the circle exactly ONE time Tangent Line: Forms a 90°angle

11. Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

12. THINGS TO REMEMBER: A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary

13. P A B C Central Angle : vertex is at the center of the circle  APB is a Central Angle

14. P A B C Case I: Vertex is AT the center

15. P E F D Semicircle: An Arc that equals 180° EDF To name: use 3 letters

16. P A B C Minor ArcMajor Arc Less than 180° More than 180° AB ACB Central Angle : vertex is at the center of the circle

17. Examples: m  1=______mAB=______m  1=______ 130°80°150°

18. measure of an arc = measure of central angle A B C Q 96  m AB m ACB m AE E = = = 2x + 14 Find x. 96° 264° x = 35

19. How do you find the measure of an angle whose vertex is ON the circle? E <DEF is called an inscribed angle because it is formed by two _______ with a common endpoint on the circle. The measure of an inscribed angle is equal to ___ of its ___________. chords ½intercepted arc

20. Another Inscribed angle… formed by a tangent and a chord.

21. Case II: Vertex is ON circle ANGLE ARC ANGLE ARC

22. 160  80  The arc is twice as big as the angle!!

23. Examples: 30 o 80 o 60 o 120 o 260 o 100 o

24. 120 x y Find the value of x and y

25. Skills and Assignment Book Page 399 Section 5.1 Vocabulary and Problem Set

26. Ticket Out the Door Name each of the following. Be sure to use proper notation! EC is a diameter of the circle. 1. Semicircle 2. Minor Arc 3. Major Arc 4. Central Angle Find each of the following measures on the diagram above. 5. ∠ EAD 6. 7. 8. 90 o 70 o