circle lesson plan

1. GRADE 10
DAILY
LESSON
PLAN (DLP)
School Duminag National
High School
Grade Level 10
Teacher Arlan O. Ydulzura Learning
Area
Mathematics
Teaching
Dates
and Time
1:00 pm -2:00 pm
Section Mars
Quarter Second Quarter
I. OBJECTIVES
A. Content
Standards
The learner demonstrates understanding of key concepts of circle and coordinate geometry.
B. Performance
Standards
The learner is able to formulate find solution to challenging situation involving circle and
other related terms in different disciplines through appropriate and accurate representations.
C. Learning
Competency/
Objectives
Wri Write the LC code
for each.
Learning Competency: The learners are able to derive inductively the relations among
chords, arc, central angles, and inscribe angles.
Given the materials and activities, the students will be able to do the following with at
least 75% level of accuracy.
a. Distinguish chords, central angle, inscribe angle, and arcs of a circle.
b. solve the measure of central angle and arcs of a circle,
c. show cooperation in group activity.
M10GE-IIc-1
II. CONTENT Geometry: Circles, particularly the Chords, Arcs, Central Angles, Inscribed Angles, and
finding the measure of an angle.
III. LEARNING
RESOURCES
A. References Mathematics Books
1. Teacher’s
Guide pages
Mathematics 10 TG, pp.129-132
2. Learner’s
Materials pages
Mathematics 10, LM, pp.140-141, p.151
3. Textbook
pages
Atela,M.D., et.al. Math @ Work 10. 2015: Neo Asia Publishing Inc.pp. 42-45
4. Additional
Materials from
Learning Resource
(LR) portal
PowerPoint presentation
Chalk
Chalk board
B. Other Learning
Resource
IV.
PROCEDURES
PRELIMINAR
IES
TEACHER’S ACTIVITY STUDENTS’
ACTIVITY

2. Greetings:
Prayer:
Checking of
Attendance:
Setting of
Class Rules
Good Morning class!
Please go back to sets and arrange your chair properly.
May I request everybody to please stand-up.
To formally start our class, may I call Ms/Mr.______ to lead the prayer.
You may now take your sets.
Let us check your attendance, say present if your name is called.
Before we will start our proper discussion this afternoon I have here a
set of rules and regulation that you need to follow.
Everybody kindly read.
R - aise your hand if you want to answer.
E – tiquitte must be observed.
S – tay silent during class discussions.
P – lease cooperate to all class activities.
E – ducate your teacher if errors occur..
C – lass rules must be followed accordingly.
T – turn off your mobile phone.
Our class rule is RESPECT.
Good morning
sir!
(Students do as
told.)
Thank you Sir!
(Students do as
told.)
R - aise your
hand if you want
to answer.
E – tiquitte must
be observed.
S – tay silent
during class
discussions.
P – lease
cooperate to all
class activities.
E – ducate your
teacher if errors
occur..
C – lass rules
must be followed
accordingly.
T – turn off your
mobile phone.

3. Is that clear?
Yes sir!
A. Reviewing
previous lesson
or presenting
the new lesson
You have learned in your previous topic on how to illustrate circle,
given this figure of a circle A.
What do we call if we have the 𝐸𝐹
⃡ ?
Base on the given figure what is our tangent?
How many chords we have on the given figure?
How about the radii?
Let us give three claps for those students answered my questions, ready
go!
Student 1.
Secant Sir
Student 2.
Line G Sir.
Student 3.
One Sir.
Student 4.
Three Sir.
(students do as
told)
B. Establishing a
purpose for the
lesson
This Afternoon I have an activity I will group you into three in my left
side will be the group one, the center column will be the group two, and
at the right side will be the group three. In the count of 10 choose a
leader and secretary each group. (times up)
Class, are you familiar with the game “Bring Me”?
Activity 1: Bring Me!
Direction: Bring me the objects that I am going to mention. You will be
given 30 seconds to bring me the particular object.
Ready na? Ready na?
Aha! Aha!
Objects to bring:
Coins Circular bracelet bottle cap masking/plastic tape
Now look closely at the objects you’ve brought. What can you say about
Yes Sir!
Aha! Aha!
Ready na! Ready
na!
Circular Sir!
A
.
B
C
D
E
F
G

4. their shapes?
Good observation! Based on our activities, what do you think would be
our lesson for this afternoon?
Great answer! So, our topic this afternoon is all about Circles,
particularly the Chords, Arcs, Central Angles, Inscribed Angles, and
finding the measure of an angle. But before we proceed let me first
introduce our learning objectives so that we will be guided throughout
our lesson.
Objectives
Given the materials and activities, the students will be able to do the
following with at least 75% level of accuracy.
a. Distinguish chords, central angle, inscribe angle, and arcs of a
circle.
b. solve the measure of central angle and arcs of a circle,
c. show cooperation in group activity.
Our objectives class is clear?
(Students guess
the topic based on
the activities.)
Circle Sir!
Yes Sir!
C. Presenting
examples/Insta
nces of the new
lesson
Class, what shape is this?
Very Good! Can you name these circles?
Circle Sir!
Circle P and
Circle A Sir!

5. So, this circle is called circle P and this one is circle A because a circle
is named based on its center.
Circles are a set of all points equidistant from a given point called center
and are indicated by the symbol ⊙. Example ⊙P and ⊙A.
Chords and Arcs are terms related to circle.
This illustration below shows circle B with the chords 𝐴𝐶
̅̅̅̅ and 𝐷𝐸.
̅̅̅̅̅
Now based on the illustration, can you define a chord?
Very good! Let’s give her three claps! Ready Go!
Chord
A chord is a line segment which endpoints are on a given circle.
Example: line segment AC or 𝐴𝐶
̅̅̅̅ and line segment DE or 𝐷𝐸
̅̅̅̅̅ are
chords of ⊙B.
Diameter
A diameter is any straight line segment that passes through the center of
a circle and whose end points lies on the circle. Example: in the figure
above line segment FG or 𝐹𝐺
̅̅̅̅ is a diameter of ⊙B.
Arcs
On the illustration, the curve from point D to point A
as well as the curve from point A to C and C to D
are examples of arcs, so based on the illustration,
what is an arc??
Arc is a part of a circumference of a circle. It is named by its endpoints
and can be read clockwise or counter-clockwise. The symbol for arc is
⏜. Example: The curve from point D to point A is an arc. Which can be
read as “arc DA or 𝐷𝐴
̂ ”.
Can you name the other arcs in the figure?
(Students define
chord based on
the illustration.)

6. Types of Arcs and Angles
There are various types of arcs. One of those is the semicircle.
1. Semicircle
On the illustration, 𝐴𝐸𝐶
̂ or 𝐶𝐸𝐴
̂ is a semicircle.
Now, based on that, define a semicircle.
An arc with a measure equal to one-half (
1
2
) the
circumference of the circle. Its measure is 180°. It is named using two or
three endpoints of the arc.
A diameter divides a circle into 2 semicircles. Using the same figure,
name the other semicircle.
2. Minor Arc
On the illustration, 𝐴𝐶
̂ is a minor arc. So, based on
that, what is the definition of a minor arc?
It is an arc that measure less than a semicircle or
180°. It is named using two endpoints of the arc or
three endpoints as long as it measures less than
180°.
Can you give another example of a minor arc?
Very good! What about this one. Can you
name the minor arcs of the circle B?
3. Major Arc
On the illustration,
𝑎𝑛𝑑 𝐶𝐷𝐴
̂ 𝑜𝑟 𝐴𝐷𝐶
̂ are
major arcs. Based on that figure, define major
arc.
It is an arc that measures greater than the semicircle. It measures greater
than 180° but less than 360°. To indicate the major arc, we must include
the point between the endpoints of the arc.
Can you name the other major arc?
𝐷𝐴𝐶
̂ 𝑜𝑟 𝐶𝐴𝐷
̂ ,
𝐴𝐶𝐷
̂ 𝑜𝑟 𝐷𝐶𝐴
̂ and
𝐴𝐷𝐶
̂ or 𝐶𝐷𝐴
̂.
(Students define
semicircle based
on the illustration.
𝐶𝐷𝐴
̂ 𝑜𝑟 𝐴𝐷𝐶
̂.
(Students define
minor arc based
on the illustration.
𝐷𝐴 Sir!
𝐴𝐶
̂ , 𝐶𝐷
̂ 𝑎𝑛𝑑 𝐴𝐶𝐷
̂
𝑜𝑟 𝐷𝐶𝐴
̂ Sir!
(Students define
major arc based
on the
illustration.)

7. Good! Can you identify the differences between a minor arc and a major
arc?
Inscribed angle
∠CAB is an inscribed angle. Based on the
illustration, define inscribed angle.
Inscribed angle is an angle whose vertex is
on the circle and sides contain chords of
the circle.
What’s the other name of the inscribed angle?
Intercepted Arc
Using the same illustration in inscribed angle, 𝐵𝐶
̂ is the intercepted arc
of ∠CAB. So, based on that, what is an intercepted arc?
Intercepted arc is formed when two lines go through the circumference
of the circle and share a common point, or vertex.
Central angle
Class, in the figure, can we consider ∠ABC as
an intercepted angle?
Very good! Actually class, ∠ABC is an example
of a central angle. So, how do you define a central angle?
𝐶𝐴𝐷
̂ 𝑜𝑟 𝐷𝐴𝐶
̂ 𝑎𝑛𝑑
𝐴𝐷𝐶
̂ 𝑜𝑟 𝐶𝐷𝐴
̂ Sir!
The measure of a
minor arc is less
than 180° but the
measure of the
major arc is
greater than
180° but less than
360°.
(Students define
inscribed angle
based on the
illustration.)
∠BAC Sir!
(Students define
intercepted arc
based on the
illustration.)

8. A central angle is an angle whose vertex is the center of the circle. The
sides of the angle contain two radii of the circle.
Example: Name all the central angles.
The measure of the central angle is equal to its intercepted arc. Example:
If m∠ABC=80, then 𝐴𝐶
̂ =80.
No Sir, because
the vertex is not
on the circle and
the sides does not
contain the
chords.
(Students define
Central angle
based on the
illustration.)
∠ABC or ∠CBA,
∠ABD or ∠DBA,
∠CBD or ∠DBC,
∠CBD or ∠DBC,
∠DCA or ∠ACD,
∠ADC or ∠CDA,
∠DAC or ∠CAD,
∠CDA or ∠ADC
D. Discussing new
concepts and
practicing new
skills # 1
In finding the measure of inscribe angle I have an example given figure
below.
Another example in finding the measure of central angle I have an
example given figure below.

9. m∠ADC=1230
, then 𝐴𝐶
̂ =1230
E. Discussing new
concepts and
practicing new
skills # 2
To learn more I have another example that will give you a knowledge in
solving the measure of an angle and the measure of arc example.
On the illustration above if we have ∠BAC = 𝐵𝐶
⏜ .
What is the m𝐵𝐶
⏜ ?
If the m𝐶𝐷
⏜ = 500
.
What is the m∠CED?
What is the m∠BAE?
This time I will teach you how to use a protractor in measuring the angle
base on the illustration below the m∠MLN = 600
Student 1.
420
Sir.
Student 2.
250
Sir.
Student 3.
1380
Sir.
.
42
o
A
B
C
D
E
500
?
?
D
1380

10. Another example:
The m∠𝑁𝐴𝑂 =900
this also called a right angle.
How about the following angles?
Group yourself into three in the count of 5 (times up), each group will
do the same task I am the one to provide a protractor. Measures the
following angles using protractor.
1. m∠𝐵𝐴𝑂
2. m∠𝑃𝐴𝐵
F. Developing
mastery
(leads to
Formative
Assessment )
Answer this illustration below in your own notebook
1. m∠𝐹𝐸𝐺
2. m𝐺𝐻
⏜
3. m∠𝐺𝐸𝐻
1.. 640
2. 1160
3. 1160
.
A
P
B N
O

11. G. Finding
practical
application of
concepts and
skills in daily
living
There are five students studied at JHcsc Dumingag Campus, each
student assign to create small a garden near in school, when they found
the area they are observe that the form/shape of the land is circular and
they are divided the area into five not equal size but they all have a
garden. The form of land the same the figure below.
I will group you into three the group each group choose a leader and
secretary and the leader will be the one to explain the output from the
group the same group in the activity 1. For the group 1 answer the
question number 1, group 2 answer the question number 2, and group 3
answer the question 3. I will give 3 minutes to answer.
1. What are the arcs of the given figure? Give at least 4.
2. How many radii from the given figure? Name all radii.
3. What are the central angle from the given figure?
Group 1.
𝐾𝑀
⏜, 𝑀𝐺
⏜, 𝐺𝐵
⏜ ,
and 𝐵𝐿
⏜
Group 2.
5 radii;
𝐵𝐹
̅̅̅̅, 𝐿𝐹
̅̅̅̅, 𝐺𝐹
̅̅̅̅,
𝑀𝐹
̅̅̅̅̅, and 𝐾𝐹
̅̅̅̅̅
∠KFM, ∠KFL,
∠LFB, ∠BFG,
∠GFM
H. Making
generalizations
and
abstractions
about the
lesson
How can you identify
a chord of a circle?
a central angle of a circle?
A chord is a line
segment which
endpoints are on a
given circle.
A central angle is
an angle whose
vertex is the
center of the
.F
B G
L
K
M

12. an inscribe angle of a circle?
an intercepted arc of a circle?
minor and major arc of a circle?
How can relate the measurement between central angle and its arc?
What about the inscribe angle to intercepted arc?
How can you distinguish if it is minor arc or major arc?
Do you think helpful to you use of protractor in getting the measure of
an angle?
circle.
Inscribed angle is
an angle whose
vertex is on the
circle and sides
contain chords of
the circle.
Arc is a part of a
circumference of
a circle.
The measure of a
minor arc is less
than 180° but the
measure of the
major arc is
greater than
180° but less than
360°.
We can relate that
the measure of
central angle of
its arc are equal.
The measure of
inscribe angle is
½ the measure of
intercepted arc.
We can
distinguish
according to the
measure of its arc.

13. Yes, because by
using a protractor
I can found the
value of the angle
in circle.
I. Evaluating
learning
Short Quiz
Test I. Read and understand each item carefully. Encircle the letter of
the correct answer.
1. An angle whose vertex is on the circle and sides contain chords of the
circle.
a. chords b. Inscribed angle
c. intercepted arc d. central angle
2. It is an arc that measures greater than the semicircle. It measures
greater than 180° but less than 360°.
a. Major arc b. minor arc
c. central angle d. semicircle
3. An angle whose vertex is the center of the circle.
a. major arc b. minor arc
c. central angle d. semicircle
4. It is a line segment which endpoints are on a given circle.
a. arcs b. chords
c. radius d. semicircle
5. A part of a circumference of a circle.
a. central angle b. chords
c. radius d. arcs
Test II
Answers
1. b
2. a
3. c
4. b
5. d
6. 𝐸𝐶
̅̅̅̅ and 𝐷𝐶
̅̅̅̅ or
𝐶𝐸
̅̅̅̅ and 𝐶𝐷
̅̅̅̅
7. ∠ECD or
∠DCE
8. ∠BAC or
∠CAB
9. a
10. c

14. For items 6-8. From the illustration, name all that describe of the
following terms.
6. chords
7. Inscribed angle
8. central angles
For items 9-10, refer to the figure above.
9. If the intercepted arc 𝐷𝐸
̂ =30° and 𝐸𝐵
̂ =88°. What is the measure of
𝐷𝐸𝐵
̂?
a. 118° b. 128° c. 125° d. 120°
10. If the measure of 𝐵𝐶
̂ =92°, what is m∠BAC?
a. 110° b. 188° c. 268° d. 180°
J. Additional
activities for
application or
remediation
Assignment: (
1
2
sheet of paper) Given the circle O below, name the
following: (Be sure to use proper notation).

15. _______1. 1 semicircle
_______2. 1 inscribed angle
_______3. at least 2 major arcs
_______4. at least 2 central angles
_______5. at least 2 chords
_______6. at least 2 minor arcs
_______7. At least 2 intercepted arc
V. REMARKS
VI.
REFLECTION
Reflect on your teaching and assess yourself as a teacher. Think about your students’
progress this week. What works? What else needs to be done to help the students learn?
Identify what help your instructional supervisors can provide for you so when you meet
them, you can ask them relevant questions.
A. No. of
learners who
earned 80% in the
evaluation
B. No. of learners
who require
additional
activities for
remediation
who scored
below 80%
C. Did the
remedial
lessons work?
No. of learners
who have
caught up with
the lesson
D. No. of learners
who continue
to require
remediation
E. Which of my
teaching
strategies
worked well?
Why did these

16. work?
F. What
difficulties did
I encounter
which my
principal or
supervisor can
help me solve?
G. What
innovation or
localized
materials did I
use/discover
which I wish to
share with
other teachers?