1. Warm-up
Find the measure of each arc.

2. Homework Review

3. EOCT Review
A gazebo is to be constructed between three houses so that it will approximately be the same distance from each house.  Which would be helpful in deciding where to locate the gazebo?    
a) Centroid
b) Circumenter
c) Incenter
d) Orthocenter b

4. CCGPS Geometry Day 21 (9-5-13)
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:
How do we use angle measures to find measures of arcs?
Standard: MMC9-12.G.C.2

5. Inscribed Angles

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

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

8. Determine whether each angle is an inscribed angle
Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
NO; QVR 2. Q V K R S

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

10. What do we call this type of angle? What is the value of x?
How do we solve for y?
The measure of the inscribed angle is HALF the measure of the inscribed arc!!
120 x y

11. 40  112  Examples 3. If m JK = 80, find m JMK.
4. If m MKS = 56, find m MS.
112  M Q K S J

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

13. x = 3 In J, m3 = 5x and m 4 = 2x + 9. Example 5
Find the value of x. 3 Q D J T U 4
x = 3

14. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

15. 2 Column Proof

16. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

17. y = 70 z = 95 110 + y =180 z + 85 = 180 Example 8 Find y and z. z 110

18. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
180
diameter

19. Example 6
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
4x – 14 = 90 H K
x = 26 N G

20. Example 7
In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x.
6x – 5 + 3x – 4 = 90 H 2 K
x = 11 1 N G

21. Practice
Worksheet

22. Homework:
Worksheet