chapter 10 circles section 10.1 goal – to identify lines and segments related to circles to use...
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Chapter 10 CirclesSection 10.1
Goal – To identify lines and segments related to circles To use properties of a tangent to a circle
Circle
Circle - The set of all points in a plane that are equidistant from a given point called the center “C”.
d = 2r
If two circles are congruent, then they have the same ___________.
r
dC
Vocabulary Chord – a segment whose endpoints are points on the circle.
Secant – a line that intersects a circle in two points.
Tangent – a line that intersects the circle in exactly one point.
Diameter – the distance across the circle through the center.
Radius – the distance from the center to a point on the circle.
Example:
Name a chord, secant, tangent, diameter and radius.
Q
R
P
T
N
S
V j
k
Intersecting Circles
In a plane, two circles can intersect in two points, one point, or not points.
Two points of intersection
One point of intersection (tangent circles)
No points of intersectioninternally tangent
externally tangent
common centers
Concentric circles
Common Tangents of Two Circles
Common Internal Tangents
n
B
A
DC m
j
k
Common External Tangents
j is a common internal tangent because it intersects the segment that joins the centers of the two circles.
m is a common external tangent because it does not intersect the segment that joins the centers of the two circles.
Theorem 10.1 & 10.2If l is tangent to circle Q at point P, then l QP
Q
P
l
If at P, then is tangent to circle Q. - Conversel l QP
Theorem 10.3If and are tangent to P, then __________SR ST
;<;<<;<<;<<;<<;<<;<<;<<;<<;<<;<<;<<;<<;< <;<
P
T
S
SR .ST
R
Example Is tangent to D? Why?CE
D45
43
11
E C
Example Given: Point E is a point of tangency.
Find: Radius, r
D
14
28
r
E
r
Example Given: and are tangents to C.
Find: x
AB AD
CA
X²-4
21
B
D