1. Day 26 – Secant and Tangent Angles
Analytic Geometry for College Graduates

2. What are we learning today?
MCC9-12.G.C.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles.
MCC9-12.G.C.4: Construct a tangent line from a point outside a given circle to the circle.
Objectives for today!
Construct a tangent line from the perimeter of the circle
Identify the vertex
Identify whether the angle is a central angle, an inscribed angle, an angle made by 2 chords, 2 secants, a chord and a secant, or 2 tangents
Find the measure of the angle depending on the location of the vertex

3. Let’s Review: Make sure you are following along as we complete the table below together as a class.
360
lines
circle 2

4. Review Continued
circle 1
perpendicular
circle

5. Case I: Vertex is AT the centerP C B

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

7. Case III: Vertex is INSIDE circle
ARC B
ANGLE D
ARC C
Be sure to emphasize that the angles is directly across from the arcs…. Big problem last year
Looks like a PLUS sign!

8. Case IV: Vertex is OUTSIDE circle
ANGLE
small ARC A
LARGE ARC D B

9. It’s all about the location of the vertex!
What does each case have in common?
It’s all about the location of the vertex!

10. Guided Practice: Identifying the Vertex
Directions: Circle the vertex in each of the following problems
Now that you have identified the vertex, let’s label the vertex as either ON the circle, INSIDE the circle, OUTSIDE the circle, or at the CENTER of the circle.

11. vertex
vertex
Angle = arc
Arc = angle 2

12. Ex. 1 Find m1. 1
84°
m<1 = 42

13. 202°
Ex. 2 Find m1. 1
m<1 = 79

14. Ex. 3 Find m1.
93° A B 1 D C
113°
m<1 = 103

15. Ex. 4 Find mQT. N Q 84 92 M T
mQT = 100

16. Ex. 5 Find x.
45
93 xº
89
x = 89

17. Ex. 6 Find m1. 1
15° A D
65° B
m<1 = 25

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

19. Ex. 8 Find m1.
260° 1
m<1 = 80