1. SECTION 10.6 –
SECANTS, TANGENTS AND ANGLE
MEASURES

2. SECANTS, TANGENTS AND ANGLE MEASURES
 How do I find the measures of angle formed by
lines intersecting on or inside a circle?
 How do I find the measures of angles formed by
lines intersecting outside the circle?

3. SECANT
 Secant: A line that intersects a circle in exactly 2
points.

4. SECANTS VS. TANGENTS
 Know the difference!

5. THEOREM
 Theorem 10.12: If two secants intersect in the
interior of a circle, then the measure of the angle
formed is one-half the sum of the measure of the
arcs intercepted by the angle and its vertical angle.

6. THEOREM
 Theorem 10.13: If a secant and a tangent intersect
at the point of tangency, then the measure of each
angle formed is one-half the measure of the
intercepted arc.

7. THEOREM
 Theorem 10.14: If two secants, a secant and a
tangent, or two tangents intersect in the exterior of
a circle, then the measure of the angle formed is
one-half the positive difference of the measures of
the intercepted arcs.

8. THEOREM 10.14
 Two secants

9. THEOREM 10.14
 A secant and a tangent

10. THEOREM 10.14
 Two tangents meeting outside the circle

11. EXAMPLE

F
88°
G
4
3
E
H
76°

12. EXAMPLE

R
P
Q
S
114°
136°
T

13. EXAMPLE
 Find x.
55°
6x°
40°

14. EXAMPLE
 A jeweler wants to craft a pendant with the shape
shown. Use the figure to determine the measure of
the arc at the bottom of the pendant.
40°

15. HOMEWORK
 Page 564
 #3 – 7
 12 - 32

16. LESSON PLAN
 Intro
 Define a secant. Define secant and tangents
relationships to a circle’s arcs
 Standards- 9.6
 Supplies – slides, whiteboard, note sheets
 Timing: One day for notes, one day for a combined
review of 10.5, 10.6 and 10.8, followed by a quiz.
 Day 1:
 Essential Questions- slides 2
 Input-slides 3 - 7
 Guided Practice - slides 8 - 15
 Independent Practice – Book Work