Notes 10A: Circles Terminology and Tangents to Circles
Vocabulary:
*A circle is the set of all points in a plane that are
equidistant from a given point, called the center of the
circle.
*The distance from the center to a point on the circle is
the radius of the circle.
*A radius is a segment whose endpoints are the center of the
circle and a point on the circle.
*Two circles are congruent if they have the same radius.
*The distance across the circle, through the center, is the
diameter of the circle.
*A chord is a segment whose endpoints are points on the
circle.
*A diameter is a chord
center of the circle.
that passes through the
*A secant is a line that intersects a circle in two points.
*A tangent is a line in the plane of a circle that intersects
the circle in exactly one point.
Theorem 10.1
If a line is tangent to a circle, then it is perpendicular to
the radius drawn to the point of tangency.
Point of tangency
Theorem 10.2
In a plane, if a line is perpendicular to a radius of a circle at
its endpoint on the circle, then the line is tangent to the
circle. (Converse of 10.1)
A common internal tangent intersects the segment that joins the
centers of the two circles. A common external tangent does not
intersect the segment that joins the centers ot the two circles.
Which is internal and which is external?
Identifying special segments and lines.
Tell whether the line or segment is best described as a chord,
secant, tangent, diameter or radius.
Diameter
en
t
er
G
A
c. BE
B
C
ng
e. BH
Ta
Tangent
Radius
et
b. DG
H
m
Radius
d. AF Secant
Di
a
a. HC
Chord
Secant
E
D
Chord
Secant
Chord
Tangent
Radius
Diameter
F
Match the notation with the term that best describes it.
A
G
B
5. C
Point of tangency
F
H
C
1. F
2. FE
Center
common internal tangent
E
3. HG
D
Radius
4. DB
common internal tangent
Center
Chord
Radius
Secant
Diameter
Point of tangency
Common external tangent
Secant
6. BE
Diameter
7. DB
Chord
8. AG
Common external tangent
If a line is tangent to a circle, then it is
perpendicular to the radius drawn to
the point of tangency.
P
O
l
Let's see if I've got this...
Line l is tangent to circle O at point P,
therefore, it is perpendicular to the radius OP.
Goal: Is RS tangent to the circle?
a 2 + b 2 = c2
92 + 122 = 152
81 + 144 = 225
225 = 225
√ It checks out!
Goal: Is RS tangent to the circle?
Finally, now
I can conclude that line
RS is tangent to circle P.
Let's Practice:
Is EF tangent to circle D?
Is BC tangent to circle A?
Keep using the Pythagorean Theorem to find lengths of missing sides.
TS is tangent to circle R.
Find the length of r if RS is 30.
YZ is tangent to circle X.
Find the length of XZ.
Using properties of Tangents
Theorem 10.3
If two segments from the same exterior point are tangent
to circle, then they are congruent.
If SR and ST are tangent to OP,
then SR ~
= ST
p
R
T
s
...more practice
Assignment
Worksheet 10A
#1­20 all
#21­33 odd