This document discusses secants, tangents, and angle measures related to circles. It defines a secant as a line that intersects a circle at two points and presents three theorems relating the measures of angles formed by secants and tangents to the measures of the arcs they intercept. Examples demonstrate using the theorems to find measures of angles and arcs. The lesson plan is to take two days, with the first day covering notes and the second reviewing related material and giving a quiz.

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