2. b.secant
Recall:
1. Define:
a. tangent
a line in the plane of a circle that
intersects the circle in exactly one point.
a line in the plane of a circle that
intersects the circle in exactly one
point.
3. c. Tangent circles
coplanar circles that intersect in
one point
d. Concentric circles
coplanar circles that have the
same center.
e. Common tangent
a line or segment that is tangent
to two coplanar circles
4. f. Common internal tangent
intersects the segment that joins
the centers of the two circles
g. Commonexternal tangent
does not intersect the segment
that joins the centers of the two
circles
5. h. Point of tangency
the point at which a tangent line intersects
the circle to which it is tangent
7. Case 1: Vertex On Circle
Find each measure:
m<BCD
mABC
8. Tangent-Chord Theorem
If a tangent and a chord intersect at a point on a circle,
then the measure of each angle formed is one half the
measure of its intercepted arc.
2
1
B
A
C
m1 =
1
2
mAB
m2 =
1
2
mBCA
12. Case 2: Vertex Inside Circle
Find the angle measure:
m<SQR
13. Interior Intersection Theorem
If two chords intersect in the interior of a circle, then the
measure of each angle is one half the sum of the
measures of the arcs intercepted by the angle and its
vertical angle.
m1 =
1
2
(mCD + mAB)
m2 =
1
2
(mAD + mBC)
2
1
A
C
D
B
14. Example 3
Find the value of x.
174
106
x
P
R
Q
S
x =
1
2
(mPS + mRQ)
x =
1
2
(106+174)
x =
1
2
(280)
x = 140
15. Try This!
Find the value of x.
120
40
x
T
R
S
U
x =
1
2
(mST + mRU)
x =
1
2
(40+120)
x =
1
2
(160)
x = 80
17. Exterior Intersection Theorem
If a tangent and a secant, two tangents, or
two secants intersect in the exterior of a
circle, then the measure of the angle
formed is one half the difference of the
measures of the intercepted arcs.
22. You try!
Remember
-Vertex On Circle = ½ measure of the arc.
-Vertex Inside Circle = ½ sum of the intercepted arcs.
-Vertex Outside Circle = ½ difference of the intercepted arcs.