2. 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 If AB is tangent to
Circle Q at point C,
then QC ⊥ AB.
A C B
3. 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
Q QF = 25
7 G NOTE: G is
NOT necessarily
D 24 F the midpoint of
QF!!
Extension: Find GF.
QF = 25 QG = 7 GF = 18
4. 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.
5. Common Tangent – a line that is
tangent to two coplanar circles.
Common Internal Tangent
Intersects
the segment
joining the
centers.
9. A
∠AOB is a
central angle
O B of circle O.
Definition: a Central Angle is an
angle with its vertex at the
center of the circle.
10. A Arcs are measured in
110° degrees, like angles.
The measure of the
intercepted arc of a
110° central angle is equal
O B
to the measure of
the central angle.
This central angle intercepts an
arc of circle O. The intercepted
arc is AB.
11. Types of arcs:
Minor Arc – measures less C
than 180° O
Example: AD
A
D
Major Arc – measures more than 180°
Example: ACD
Semicircle – measures exactly 180°
Example: ADC
**Major Arcs and Semicircles are ALWAYS
named with 3 letters.**
12. Adjacent Arcs – Two arcs that
share a common endpoint, but do
not overlap.
F AF and FE are
adjacent arcs.
E
A O EF and FAE are
adjacent arcs.
13. Name…
1.Two minor arcs Y
VW, WY
2.Two major arcs W Z
VYW, XYV , WVY
3.Two semicircles
V X
VWY, VXY
Circle Z
4.Two adjacent arcs
VW & WY or YXV & VW
14. Give the measure of each angle or arc.
1. m∠WOT = 50° Y
X
2. mWX = 100°
30°
3. mYZ = 90°
100° Z
4. mYZX = 330° O
50°
5. mXYT = 210°
W
6. mWYZ = 220°
50° T
7. mWZ = 140°
