CIRCLES AND TERMS
RELATED TO IT
MATHEMATICS 7
March 29, 2023

CONTENT STANDARD
The learner will be able to understand the key
concepts of geometry of shapes and sizes, and
geometric relationships.
PERFORMANCE STANDARD
The learner will be able to demonstrate
understanding on how to create models of
plane figures and formulate and solve
accurately authentic problems involving sides
and angles of a polygon.

• The learner illustrates a circle and the terms
related to it: radius, diameter, chord,
circumference, center, arc, central angle, and
inscribed angle.
LEARNING COMPETENCY:
1. define circle and terms related to it;
2. illustrate the different terms related to circle;
and
3. solve the circumference of a circle.
LEARNING OBJECTIVES:

• If the sum of the interior
angle of a regular polygon
is 1,0800 , how many sides
does a polygon have?
RECALL

Read me!
Last October 2020, the Philippines experienced the world’s
strongest typhoon Typhoon Rolly (internationally known as GONI)
which devastated the regions of Bicol and Central Luzon. Rolly's wide
diameter — estimated at 500 kilometers — means areas not directly
hit by the typhoon's eye can also experience similar conditions
because of its wide reach. Because of the extensive damage brought
by the typhoon in the Philippines, the Philippine Atmospheric,
Geophysical and Astronomical Services Administration (PAGASA)
announced that the name Rolly will be delisted from the list of
typhoon names and will no longer be used in the future. A
replacement name will be chosen in 2021.

CIRCLE
• A circle is the set of all
points in the plane that
are the same distance
away from a specific
point, called the center.
The center of the circle
below is point A. We call
this circle “circle A” or in
symbol, ʘA, and it is
labeled circle with center
A.

TERMS RELATED TO
CIRCLE
• Radius is a line segment connecting the
center of the circle and a point on the
circle. It is named using the letter of the
center and the point on the circle.
• (plural radii)
The ʘA has a radius of AB̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅.

TERMS RELATED TO
CIRCLE
• Chord is a line segment whose
endpoints are both on a circle. It is
named using the endpoints on the
circle.
In ʘA, the chord is BC̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅.

TERMS RELATED TO
CIRCLE
• Diameter is a chord that passes through
the center of the circle. The length of a
diameter is two times the length of a
radius.
In circle A, the diameter is DE̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅.

TERMS RELATED TO
CIRCLE
• Circumference is the distance around
the circle and can be obtained using
the formula:
• C = 2𝜋r; where r is the radius of the
circle
• or C = 𝜋D, where D is the diameter of
the circle

Illustrative Example
• What is the circumference of a circle whose
radius measures 7 cm (use π = 3.14)?
Solution:
What are the given? r = 7cm, 𝛑 = 𝟑. 𝟏𝟒
What is asked? What is the measure of the
circumference?
What operation to be used? Multiplication
Using the formula of the circumference
C = 2𝜋r
= 2(3.14) (7cm)
= 6.28(7cm)
= 43.96 cm

TERMS RELATED TO
CIRCLE
• Secant Line is a line that intersects a
circle in two points.
In ʘA, the secant is FG⃡ .

TERMS RELATED TO
CIRCLE
• Tangent Line is a line that intersect a
circle at exactly one point.
• HG⃡ is the tangent of ʘA and the point
of tangency is point J.

TERMS RELATED TO
CIRCLE
• Central Angle is an angle whose
vertex is the center of the circle.
• In ʘ A, ∠BAC is a central angle

TERMS RELATED TO
CIRCLE
• Arc is any part of the circumference of a circle. There
are three types of arcs namely:
1. Minor arc
2. Semi-circle
3. Major arc

TERMS RELATED TO
CIRCLE
1. Minor Arc is an arc whose measures is
greater than zero but less than 180o
(0o < 𝜃 < 180o). It is named using two capital
letters.
• In circle A, Arc BC or BC⏜ is a minor arc.

TERMS RELATED TO
CIRCLE
2. Semi-circle is an arc whose measure is
exactly 180o or one-half of the circle.
Semi-circle is named using 3 capital
letters.
In circle A, arc EJC or EJC ⏜ is a semi-
circle.

TERMS RELATED TO
CIRCLE
3. Major Arc is an arc whose measure is
greater than 180o but less than 360o
(180o < 𝜃 < 360o). It is named using 3
capital letters.
In circle A, arc MGS or MGS ⏜ is a major
arc.

TERMS RELATED TO
CIRCLE
Concentric Circles are two or more
circles that have the same center,
but with different radii (plural form
of radius).

TERMS RELATED TO
CIRCLE
Congruent Circles are two or more circles
with the same radius, but with different
centers.

TERMS RELATED TO
CIRCLE
Inscribed Angle is an angle whose vertex
lies on the circle.
In circle A, the inscribed angle is ∠EJC.

Example 1
Using the figure at the right, identify the parts of the circle.
A circle is named by its center. Thus, we call the circle on the
right, ⊙P.
Center:
radii:
Diameter:
chords :
arcs:
central angles :
P
𝑃𝐴̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
, 𝑃𝐶̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
, 𝑃𝐵̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝐵𝐶̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
or 𝐶𝐵̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝐷𝐸̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
, 𝐵𝐶̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
𝐶𝐴̂, 𝐴𝐵̂ , 𝐸𝐷̂ 𝐴𝐵𝐶 ̂, 𝐴𝐸𝐶 ̂, 𝐶𝐴𝐵 ̂, 𝐶𝐸𝐵 ̂
∠𝐶𝑃𝐴 , ∠𝐴𝑃𝐵

Example 2
Illustrate ⊙ 𝐵 having
a.) radius 𝐵𝐶̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
b.) diameter 𝐴𝐷̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
c.) chords 𝐸𝐷̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
& 𝐴𝐷̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
d.) arcs: 𝐷𝐶̂ , 𝐶𝐴̂, 𝐴𝐸̂ , 𝐷𝐶𝐴 ̂ , 𝐷𝐸𝐴 ̂ e.) central angles: ∠𝐴𝐵𝐶, ∠𝐶𝐵𝐷
f.) inscribed angle: ∠𝐴𝐷𝐸

Using the figure at the right, which term that is
related to circle . Choose you answer in box below.
1. EJ ⃡ ____________________
2. ̅̅̅̅EN̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ____________________
3. ̅̅̅̅ER̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ____________________
4. IR̅̅̅̅̅̅̅̅̅̅̅̅ ____________________
5. IW⃡ ____________________
6. Point E ____________________
7. IEW⏜ ____________________
8. IE⏜ ____________________
9. IER⏜ ____________________
10. Point N ____________________

Refer to the given circle below. Answer what is
asked. The first one is done for you.

Thank You