Introduction
to Circles
Michael A. Corpuz
Circles - Terms
y
90°
180°
Radius (r)
Center
Chord
270°
Circumference = 2πr = dπ
x
0°
Vocabulary
• Circle – the locus (set) of all points in a plane
equidistant for a given point
• Center – the central point of a circle
• Chord – any segment that endpoints are on
the circle
• Diameter – a chord that passes through the
center of the circle
• Radius – any segment that endpoints are the
center and a point on the circle
• Circumference – perimeter of a circle
a. Name the circle.
Answer: The circle has its center at E, so
it is named circle E, or
.
b. Name the radius of the circle.
Answer: Four radii are shown:
.
c. Name a chord of the circle.
Answer: Four chords are shown:
.
d. Name a diameter of the circle.
Answer:
are the only chords that go through
the center. So,
are diameters.
a. Name the circle.
Answer:
b. Name a radius of the circle.
Answer:
c. Name a chord of the circle.
Answer:
d. Name a diameter of the circle.
Answer:
Circle R has diameters
a. If ST = 18, find RS.
and
.
Formula for radius
Substitute and simplify.
Answer: 9
b. If RM = 24, find QM.
Formula for diameter
Substitute and simplify.
Answer: 48
c. If RN = 2, find RP.
Since all radii are congruent, RN = RP. Answer: So, RP = 2.
Circle M has diameters
a. If BG = 25, find MG.
Answer: 12.5
b. If DM = 29, find DN.
Answer: 58
c. If MF = 8.5, find MG.
Answer: 8.5
Theorems
• If a radius is perpendicular to a
chord, then it bisects the chord.
• If a radius of a circle bisects a chord
that is not a diameter, then it is
perpendicular to the chord.
• The perpendicular bisector of a
chord passes through the center of
the circle.
Congruent Circles – Circles
that have congruent radii.
Concentric Circles – Coplanar
circles having the same center.
Theorems
• If a chords of a circle or of
congruent circles are equidistant
from the center(s), then the
chords are congruent
• If a chords of a circle or of
congruent circles are congruent,
then they are equidistant from
the center of the circle.
Central Angle – is an angle
whose vertex is the center of
the circle.
Minor Arc - an arc of a circle
that measures less than a
semicircle. It is named using
two capital letters, the endpoints
of an arc.
Major Arc – an arc of a circle that
measures greater than a
semicircle. It is named using 3
capital letters, the two endpoints
and another point on the arc.
Semicircle- is the union of the end
points of a diameter and all points
of the circle that lie on one side of
the diameter.
Inscribed Angle – is an angle
whose vertex lies on the circle and
whose sides contain chords of the
circle.
Activity 1
Activity 2