1. Lesson 10.6 – Secants, Tangents, and Angle Measure
Standards G.6.2, G.6.5

2. Definitions
Unlike diameters and chords, tangents and secants are lines, not line segments.
A tangent is a line which intersects a circle only once.
A secant is a line which intersects a circle twice.

3. Angle Measures
When a combination of secants and tangents are drawn in a circle, they intersect in one of three ways:
Inside the Circle
Outside the Circle
On the Circle

4. Intersection Inside Circle
Angle measures: Add the two opposite arc
measures together and divide by 2.
Arc 2
<1
<2 A B C
Arc 1
Arc 3 D
Arc 4

5. Example 1 Find m<1 B Find m<2 <2 <1 A 1700 30 + 40 = 70/2
= 350
Find m<2 2
= 290/2
400
300
= 1450
1200

6. Intersection Outside Circle
Angle measures: Large arc – small arc
divided by 2 A B
<1 D C

7. Example 2
Find x
141-62 2
= 79/2
1410 x0
620
= 39.5

8. Intersection on the Circle
Angle measures: Half of the intercepted arc
(same as inscribed angle!) A
<1 B
m<1 = arc ABC 2 C

9. Example 3
Find m<
<1 =
1500
3000

10. Example 4 Arc AB = 600 Arc BC = 500 Arc CD = 1300 Arc AD = m<1 =
<4
600
1200 B
Arc AD =
m<1 =
m<2 =
m<3 =
m<4 =
1200
<2
850
<1
<3
500
950
950 D C
550
1300

11. Practice
Marker boards