Section 9-1
Circles Vocab
Circle – the set of all points in a plane a
given distance away from a center point.
A
A circle is named by
its center point. For
example: Circle A or
A.
Radius (r) Plural: Radii
Radius – the “given distance away from
the center point” of a circle; a segment
that joins the center to a point on the
circle.
Sphere – the set of all points a given
distance away from a center point.
Chord – a segment whose endpoints lie on
on the circle.
Example: DC
A
B
C
D
Diameter – a chord that passes through
the center of the circle. Example: AB
A diameter is twice the length of a radius.
Secant – a line that contains a chord.
B
A
Example: AB
**Note: A chord and a secant can be named
using the same letters. The notation tells you
whether it is a secant or a chord. A secant is
a line; a chord is a segment.**
Secant: AB
Chord: AB
Tangent – a line that intersects a
circle at exactly one point.
B
A
Example: AB
Not a
tangent!
The point at which the
circle and the tangent
intersect is called the
point of tangency.
Example: A
5cm
5cm
Concentric
Circles – circles
with the same
center point.
Congruent Circles –
circles with
congruent radii.
When each vertex of a polygon
is on the circle, the circle is said
to be circumscribed around the
polygon.
This circle is
circumscribed
around the
pentagon
When each side of a polygon is
tangent to a circle, the circle is
said to be inscribed in the
polygon.
This circle is
inscribed
inside of the
pentagon.
Section 9-2
Tangents
Theorem 9-1: If a line is tangent to
a circle, then the line is
perpendicular to the radius drawn to
the point of tangency.
Q is the center of the circle. C is a point of tangency.
Q
A
C
B
If AB is tangent to
Circle Q at point C,
then QC ^ AB.
Example: Given Circle Q with a radius length of
7. D is a point of tangency. DF = 24, find the
length of QF.
72 + 242 = QF2
QF = 25
Q
7
D
G
24
F
Extension: Find GF.
QF = 25
QG = 7
NOTE: G is
NOT necessarily
the midpoint of
QF!!
GF = 18
Theorem 9-2: If a line in the plane
of a circle is perpendicular to a
radius at its outer endpoint, then
the line is tangent to the circle.
This is the converse of Theorem 9-1.
Tangent Circles – coplanar
circles that are tangent to the
same line at the same point.
Internally
Tangent Circles
Externally
Tangent Circles
Common Tangent – a line that is
tangent to two coplanar circles.
Common Internal Tangent
Intersects
the segment
joining the
centers.
Common External Tangent
Does not intersect the
segment joining the
centers.