Unit 8 Essential Questions
• What is the difference between tangent, chord
and secant lines and how do they relate to
segment lengths in a circle?
• How are arc measures related to central,
inscribed, and circumscribed angles?
Unit 8 Bonus Question
• Will be posted on website shortly
Today’s Objective
11-1 Tangent Lines
• Students will be able to use the
relationship between a radius and a
tangent.
• Students will be able to use the
relationship between two tangents from
one point.
Circle
• Definition: A circle is a set of points equidistant
from a given point.
• Name:
Radius
• Definition: A segment with one endpoint at
the center and one endpoint on the circle.
(Plural of Radius)
• Note: All radii of the
same circle are congruent!
Tangent of a Circle
• Definition: A Tangent Line is a line that
touches a circle at exactly one point.
• Definition: A Point of Tangency is the
point where the tangent line touches the
circle.
O
B
A
Theorem 1
• If a line is tangent to a circle, then it is
perpendicular to the radius at the point of
tangency
O
B
A
Theorem 2
• Two tangent segments from the same
point are congruent
M
L
N
Example 1 – Find x
• Assume that lines that appear to be tangent are
tangent
15
x
12
Example 2 – Find x
• Assume that lines that appear to be tangent are
tangent
L
O
117°
x°
N
M
Example 3 – Find x
• Assume that lines that appear to be tangent are tangent
H
16
x
I
G
8
Example 4 – Find MN
• Assume that lines that appear to be tangent are tangent
O
35
P
8
14
N
M
Inscribed vs Circumscribed
• A figure is INscribed in another figure if it is
completely INside the other figure.
• The circle is inscribed in the triangle
• A figure is circumscribed about another figure
if it completely surrounds the other figure.
• The circle circumscribes the triangle
Example 5
• The circle is inscribed in ∆ABC. Find the perimeter of ∆ABC
• Hint: Apply Thm 2
Classwork
• Arrange desks in groups
• As a group, complete page 3 of Unit 8
packet (Practice 11-1)
• Be prepared to have your work displayed
on doc cam!
Homework
• Complete page 3 of Unit 8 Packet
(Practice 11-1)