Define parts of a circle Apply properties of lines tangent to a circle

1. Circle Vocabulary and Tangents
The student is able to (I can):
• Define parts of circles
• Apply properties of lines tangent to a circle

2. circlecirclecirclecircle – the set of all points in a plane that are a fixed distance
from a point, called the center.
A circle is named by the symbol and its center.
A
•
A

3. diameterdiameterdiameterdiameter – a line segment whose endpoints are on the circle
and includes the center of the circle.
radiusradiusradiusradius – a line segment which has one endpoint on the circle
and the other on the center of the circle.
A
•
C
B
D
CD is a diameter
AB is a radius

4. secantsecantsecantsecant – a line that intersects a circle at two points
chordchordchordchord – a line segment whose endpoints are on the circle. (A
diameter is a special kind of chord.)
tangenttangenttangenttangent – a line in the same plane as a circle that intersects it
at exactly one point.
pointpointpointpoint ofofofof tangencytangencytangencytangency – the point where the tangent and a circle
intersect.
•
A
B
m
C
chord
secant
tangent
point of
tangency

5. commoncommoncommoncommon tangenttangenttangenttangent – a line that is tangent to two circles.
common external tangent
common internal tangent

6. Theorem: If a line is tangent to a circle, then it is
perpendicular to the radius drawn to the point of tangency.
Theorem: If a line is perpendicular to a radius at a point on
the circle, then it is tangent to the circle.
This property lends itself to lots of problems involving
right triangles.
BELine t ⊥
Line t tangent
to ⊙B •B
E
t

7. Theorem: If two segments are tangent to a circle from the
same external point, then the two segments are congruent.
•
S
A
N
D
SD ND≅

8. Examples
The segments in each figure are tangent. Find the value of
each variable.
1.
2.
•
2a + 4
5a – 32
•
6y2 18y

9. Examples
The segments in each figure are tangent. Find the value of
each variable.
1.
2.
•
2a + 4
5a – 32
•
6y2 18y
5a – 32 = 2a + 4
3a = 36
a = 12
6y2 = 18y
y y
6y = 18
y = 3