1. Lesson 9.2A R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

2. Intercepted Arc A piece of a circle contained between the two rays of an angle Central Angle An angle inside a circle with its vertex at the center of the circle Inscribed Angle An angle inside a circle with its vertex on the circle

3. Arc measures always given in degrees. The measure of a central angle is equal to the measure of the intercepted arc. The measure of the inscribed angle is one half of the measure of the intercepted arc. A tangent line is always perpendicular to the radius or diameter drawn to the point of tangency.

4. Find the value of the variables: xoxo A C B xoxo A C B 30 O

5. Find the value of the variables: 150 o A B xOxO yoyo A C B 60 O

6. Given that AB is tangent to the circle, find the value of x. 37 o xoxo A B C

7. Given that CD is tangent to the circle, find the value of x. xoxo 72 o C D E

8. Given that AB and AD are both tangent to the circle, find the value of x. 140 o xoxo A B D C

9. Given that PQ and PS are both tangent to the circle, find the value of x. 150 o xoxo P Q S T

10. Remember, the radius of a circle never changes, regardless of what point on the circle it’s drawn to.

11. Find the value of x, given circle O and the following segment lengths: AC = 16, OB = 12, OE = x. If your answer is not an integer, round to the nearest tenth. x AC B O E

12. Find the value of x, given circle O and the following segment lengths: AC = 50, OB = 20, OE = x. If your answer is not an integer, round to the nearest tenth. x AC B O E

13. Find the value of x, given circle P and the following segment lengths: MN = 35, PS = 10, ST = x. If your answer is not an integer, round to the nearest tenth. M N S P T

14. Find the value of x, given circle P and the following segment lengths: MN = 18, PS = 5, ST = x. If your answer is not an integer, round to the nearest tenth. M N S P T