Transcript Lesson 1 Contents

5-Minute Check on Lesson 10-5
Transparency 10-6
Determine whether each segment is tangent to the given circle.
1. BC
2. QR
Yes
No
Find x. Assume that the segments that appear to be tangents are
tangents.
3.
4.
x = 20√5
or 44.72
x = 12
5.
Standardized Test Practice:
A
10
B
12
C
What is the measure of PS?
14
D
18
Click the mouse button or press the
Space Bar to display the answers.
Lesson 10-6
Secants, Tangents, and Angle
Measures
Objectives
• Find measures of angles formed by lines
intersecting on or inside a circle
• Find measures of angles formed by lines
intersecting outside a circle
Vocabulary
• Secant – a line that intersects a circle in
exactly two points
Circles – Secants
y
Interior Angles
formed by a Secant & a Tangent
m3 = ½ (m Arc JMK)
m4 = ½ (m Arc JLK)
M
3
1
2
4
K
x
J
P
Center
Interior Angles
formed by 2 Secants
m1 = ½ (m Arc MJ + m Arc LK)
m2 = ½ (m Arc MK + m Arc JL)
L
Circles – External Angles
Two Secants
Secant & Tangent
J
J
L
K
J
K
T
N
Two Tangents
M
M
M
S
T
mJ = ½(m Arc TM – m Arc TK)
mJ = ½|m Arc TM – m Arc TK|
mJ = ½(m Arc MN – m Arc LK)
mJ = ½|m Arc MN – m Arc LK|
mJ = ½(m Arc TMS – m Arc TS)
mJ = ½|m Arc TMS – m Arc TS|
Find
Method 1
if
and
Method 2
Answer: 98
Find
if
Answer: 138
and
Find
Answer: 55
if
and
Find
Answer: 58
if
and
Find x.
Theorem 10.14
Multiply each side by 2.
Add x to each side.
Subtract 124 from each side.
Answer: 17
Find x.
Answer: 111
JEWELRY 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.
Let x represent the measure of the arc at the
bottom of the pendant. Then the arc at the top
of the circle will be 360 – x. The measure of the
angle marked 40° is equal to 1/2 the difference
of the measure of the two intercepted arcs.
Multiply each side by 2 and
simplify.
Add 360 to each side.
Divide each side by 2.
Answer: 220
PARKS Two sides of a fence to be built around a
circular garden in a park are shown. Use the figure
to determine the measure of
Answer: 75
Find x.
Multiply each side by 2.
Add 40 to each side.
Divide each side by 6.
Answer: 25
Find x.
Answer: 9
Summary & Homework
• Summary:
– The measure of an angle formed by two secant
lines is half the positive difference of its
intercepted arcs
– The measure of angle formed by a secant and
tangent line is half its intercepted arc
• Homework:
– pg 564-566; 12-14, 18-20; 23-24, 26, 29, 34-36