3. 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 or 3 letters To name: use 3 letters <APB is a Central Angle

4. P E F D Semicircle: An Arc that equals 180° EDF To name: use 3 letters EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°

5. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Congruent Linear Pairs are Supplementary Opposite angles of a quadrilateral are supplementary

6. Vertical Angles are Equal

7. Linear Pairs are Supplementary http://www.mathopenref.com/linearpair.html 120°60°

8. Point of tangency – the point at which a tangent line intersects the circle to which it is tangent point of tangency Definition

9. In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

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

11. Arc Addition Postulate A B C m ABC = m AB + m BC

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. Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. 45 A B C D 110

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

15. Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. C L O T 1. YES; CL

16. Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. Q R K V 2. YES; QVR S

17. 160° 80° To find the measure of an inscribed angle…

18. x y 45 78 110 w z If a quadrilateral is inscribed in a circle, then opposite angles are supplementary.

19. 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!!

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

21. 72  If two inscribed angles intercept the same arc, then they are congruent.

22. Example 5 In  J, m< A= 5x and m< B = 2x + 9. Find the value of x. A Q D J T U B m<A = m<B 5x = 2x+9 x = 3

23. 94 s n Given circle A find values of s and n A

24. 32 14 a b c d e f g h Find the values of the variables.