3. Page 3
Definition
"The set of all points equidistant
from the center".
The locus of all points a fixed
distance from a given (center) point.
4. Page 4
Terms related to a circle
Center - a point
inside the circle
from which all
points on the circle
are equidistant
Radius - the
distance from the
center to any point
on the circle.
5. Page 5
Terms related to the circle
Chord - a line
segment joining any
two points on a
circle.
Diameter - a chord
passing through the
center.
6. Page 6
Terms related to the circle
•Tangent - A line
passing a circle and
touching it at just
one point.
•Secant - A line that
intersects a circle at
two points.
7. Page 7
Terms related to a circle
ARC – a subset of
a circle
Minor Arc < 180°
Major Arc > 180°
Semicircle = 180°
8. Page 8
Terms related to a circle
Central Angle –
angle made by two
radii
Inscribed Angle –
angle made by two
chords intersecting
ON a circle
9. Page 9
Terms related to a circle
•Circumference - the
distance around the
circle. Strictly
speaking a circle is
a line, and so has no
area.
•What is usually
meant is the area of
the region enclosed
by the circle.
10. Page 10
1 Kings 7:23-24 (New
American Standard Bible)
23
Now he made the sea of cast
metal ten cubits from brim to
brim, circular in form, and its
height was five cubits, and thirty
cubits in circumference.
24
Under its brim gourds went
around encircling it ten to a
cubit, completely surrounding
the sea; the gourds were in two
rows, cast with the rest.
Even the bible had an approximation for pi! =)
11. Page 11
Terms related to a circle
Segment of a circle
– region on the
circle bounded by a
chord and an arc
Sector – region
bounded by a
central angle and an
arc
19. Page 19
R K
P
M
Given circle P below, what name applies
to each of the following?
20. Page 20
Indicate whether each statement is TRUE or FALSE.
Every diameter of a circle is a secant of the
circle.
Every radius of a circle is a chord of the
circle.
Every chord of a circle contains exactly two
points of the circle.
If a radius bisects a chord of a circle, then it is
⊥ to the chord.
21. Page 21
Indicate whether each statement is TRUE or FALSE.
The intersection of a line with a circle may be
empty.
A line may intersect a circle in exactly one
point.
The secant which is a perpendicular bisector
of a chord of a circle contains the center of the
circle.
23. Insights on the Shortest Distance
TSDB2P = The Shortest Distance
Between 2Points
In geometry, TSDB2P is a straight
line.
In sickness, TSDB2P is relief.
24. Insights on the Shortest Distance
TSDB2P = The Shortest Distance Between 2Points
In deep poverty, TSDB2P is realizing you
have plenty to give.
In a career, TSDB2P is integrity.
In parenting, TSDB2P is allowing them to
grow from their own mistakes.
25. Insights on the Shortest Distance
TSDB2P = The Shortest Distance Between 2Points
In friendship, TSDB2P is trust.
In learning, TSDB2P is a mind awaiting
discovery.
In personal growth, TSDB2P is learning
your lesson the first time.
26. Page 26
Inscribed Angle
Theorem
The measure of an
inscribed angle is
equal to one-half
the degree measure
of its intercepted
arc.
27. Page 27
Central Angle
Theorem
The central angle is
twice the inscribed
angle.
28. Page 28
Intersecting Chord
Theorem
When two chords
intersect each other
inside a circle, the
products of their
segments are
equal.
B
A C
D
E
29. Page 29
Angle Formed by
Intersecting
Chords
m∠ABC =
____________________
B
A C
D
E
30. Page 30
Intersecting
Secants Theorem
When two secant
lines intersect each
other outside a
circle, the products
of their segments
are equal.
A
B
C
D
E
31. Page 31
Angle Formed by
Intersecting
Secants
m∠ACE =
________________
A
B
C
D
E
33. Page 33
Angle Formed by
Intersecting
Tangents
m∠BCA =
______________
A
B
C
D
34. Page 34
Intersecting
Tangent & Secant
Theorem
When two secant
lines intersect each
other outside a
circle, the products
of their segments
are equal.
A
B
C
D
38. Page 38
In the figure, M is the center of the circle.
Name a central angle.
Name a chord that is not
a diameter
Name a major arc.
If m∠KMI = 170°, what
is mKGI ?
What is m∠KHI ?
M
K
G
I H
39. Page 39
Problem: Find the value of x.
Given: Segment AB is tangent to circle C at B.
40. Page 40
Find the measure of each arc/angle:
arc QSR ∠Q ∠R
41. Page 41
Name the arc/s intercepted by:
∠x ∠y ∠z
x
y
z
R
Q
S
P
T
V
A
42. Page 42
Sometimes, secants intersect outside of circles. When
this happens, the measure of the angle formed is equal
to one-half the difference of the degree measures of the
intercepted arcs.
Find the measure of angle 1.
Given: Arc AB = 60o
Arc CD = 100o
44. Page 44
Commonly Used Reasons
Radii of the same circle are congruent.
Base angles of an isosceles triangle are
congruent.
The exterior angle is equal to the sum of the
remote interior angles.
The degree measure of a minor arc is equal to
the measure of the central angle which
intercepts the arc.
45. Page 45
If an angle is inscribed in a circle, then the
measure of the angle equals one-half the
measure of its intercepted arc. (page 170)
P
x
R
Q
S
46. Page 46
PROOF:
STATEMENTS REASONS
Given
Radii of the same circle
are congruent
3. ∆QRS is an isosceles ∆ Def. of an isosceles ∆
4. ∠PQR ≅ ∠QRS Base angles of an
isosceles ∆ are ≅
47. Page 47
PROOF:
STATEMENTS REASONS
5. m∠PQR = m∠QRS Def. of ≅ angles
6. m∠QRS = x Transitive Property
7. m∠PSR = 2x Central Angle Thm.
The minor arc ….
53. Page 53
A tangent to a circle is ________________
to the radius at the point of tangency.
perpendicular
54. Page 54
Properties of Tangents
Tangent segments to a
circle’s circumference
from any external point
are _______________.
The angle between the
tangent and the chord is
____________________
the intercepted arc.
half of the measure of
congruent
The angle between the
tangent and the chord is
_________________the
inscribed angle on the
opposite side of the
chord.
equal to
