Circles
Diameter
Chord
Central Angle
Semicircle
Tangent
Inscribed Angle
R10
Radius
Secant
Major Arc Minor Arc
Angle Rules
Central
O
Rule: ____________________
Inscribed
.O
1
Rule: ____________________
.O
2
Tangent and a Chord
.O
Rule: ____________________
Arcs and Parallel Chords
Intersecting Chords
.O
Rule: __________________
Rule:_______________
Tangents and Secants
Rule:____________________
A Tangent and a Secant
.
O
Two Tangents
.O
Two Secants
.O
R10
1.
In the diagram below, trapezoid ABCD, with bases
with diameter
2.
. If
In the diagram below of circle O, chords
In the diagram below of circle O, chords
ABC  28 and
, is inscribed in circle O,
, find ADC .
. What is the degree measure of
3.
and
and
intersect at E,
, and
?
and
intersect at point B, such that
ª ?
. What is AC
x
28 
R10
4.
In the diagram below, tangent
is
5.
. Find
, what is
are drawn to circle O. The ratio
.
In the diagram of circle O below, chords
of the circle. If
6.
and secant
and
are parallel, and
is a diameter
?
In the diagram below, two parallel lines intersect circle O at points A, B, C, and
D, with
and
. Find
.
R10
Length Rules
C
Intersecting Chords
A
E
B
Rule:_______________________
D
Common Tangents
Rule:_______________________
Lengths of Tangents and Secants
Two Secants
Tangent and a Secant
Rule:____________________
Rule:_______________________
1.
In the diagram of circle O below, chord
intersects chord
,
, and
. What is the value of x?
at E,
,
R10
2.
In the diagram below of circle O, diameter
If
and
, find the length of
.
is perpendicular to chord
3.
In the diagram below of circle O, chord
bisects chord
find the length of
in simplest radical form.
4.
In the diagram below of circle O, radius
is 5 cm. Chord
is 8 cm and is
perpendicular to
at point P. What is the length of
, in centimeters?
at E. If
and
at E.
,
R10
5.
How many common tangent lines can be drawn to the two externally tangent circles
shown below?
6.
In the diagram below,
respectively,
,
7.
8.
,
, and
, and
are tangents to circle O at points F, E, and D,
. What is the perimeter of
?
In the diagram below, circles X and Y have two tangents drawn to them from external
point T. The points of tangency are C, A, S, and E. The ratio of TA to AC is 1:3.
If TS = 24, find the length of SE.
In the diagram below, tangent
and secant
are drawn to circle O from external
point P. If
and
, what is the length of
?
R10
9.
In the diagram below of circle O, chords
tangent
,
10.
and
intersect at M. Secant
and
are drawn to circle O. The length of
is two more than the length of
,
, and
. Find the length of
. Find the length of
.
In the diagram below of circle O, secant
intersects circle O at E,
,
of
?
Equations of Circles
intersects circle O at D, secant
, and
. What is the length
r
 (h,k)
R10
Center at the origin (0,0)
with radius r units.
_________________
1.
Center at the point (h, k)
with radius r units.
_________________
What are the center and the radius of the circle whose equation is
?
2.
Write an equation for each circle whose center is (-3, 2) and whose diameter is 10.
3.
Write an equation represents the circle whose center is
4.
A circle is represented by the equation
. What are the coordinates of
the center of the circle and the length of the radius?
5.
Write an equation for the circle shown in the graph below?
and whose radius is 5?
R10
6.
Write the equation represents circle K shown in the graph below?
7.
Write an equation of the circle graphed in the diagram below.
8.
What is an equation of a circle with its center at
and a radius of 4?