Class 9 Exam > Class 9 Videos > Equal chords subtend equal angles at the center of a circle (Theorem and proof)
Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9
FAQs on Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9
| 1. What is the theorem about equal chords subtending equal angles at the center of a circle? |  |
Ans. The theorem states that if two chords of a circle are equal in length, then they will subtend equal angles at the center of the circle.
| 2. How can I prove the theorem about equal chords subtending equal angles at the center of a circle? | |
Ans. The proof of this theorem can be done by using the properties of angles formed by chords in a circle. By drawing radii from the center of the circle to the endpoints of the chords, we can form two congruent triangles. Using the congruence of these triangles, we can conclude that the angles subtended by the chords at the center are equal.
| 3. Can you give an example to demonstrate the theorem about equal chords subtending equal angles at the center of a circle? | |
Ans. Sure! Let's consider a circle with two chords AB and CD. If AB and CD have the same length, we can draw radii from the center O to the endpoints of the chords. This forms two congruent triangles, AOB and COD. Therefore, the angles AOB and COD, which are subtended by the chords at the center, are equal.
| 4. What is the significance of the theorem about equal chords subtending equal angles at the center of a circle? | |
Ans. This theorem is significant because it helps us understand the relationship between the lengths of chords in a circle and the angles they subtend at the center. It allows us to make connections between the geometry of the circle and its algebraic properties, enabling us to solve various problems involving circles.
| 5. Are there any real-life applications of the theorem about equal chords subtending equal angles at the center of a circle? | |
Ans. Yes, this theorem has several real-life applications. For example, it can be used in engineering and architecture to design structures with circular components such as bridges, arches, and wheels. It can also be used in navigation and GPS systems to calculate distances and angles based on the positions of satellites or landmarks on a map.
Text Transcript from Video
hello dosto welcome welcome to this
presentation from rising pearl hum apke
hosaka destroy Aquaman amigos no for
quite some time now we are discussing
series 10 called circles I just already
said number 6 now though so this is the
first theorem on circles that we are
discussing so that's all yeah the
theorem here that states that equal
chords subtend equal angles at the
centre of the circle so also theorem
again is equal chords they subtend equal
angles at the centre of the circle so
those are our chair episode number 6
Atticus waves are malcolm brog botswana
fair Shelia now let us prove why this
theorem is always true so that's the
humming cat of the ham we will just
first we will understand what the
theorem is before we jump into the proof
so if you REM is telling us equal chords
of a circle so equal chords those
pokemon oh my cards come out love hey
Coby the point of letting her circle me
and if you join them by a straight line
okay I'm getting a quad so equal chords
mullah does not make more than one
culture here so equal chords of a circle
they subtend equal angles at the centre
now Kamala Meadows the hamari last
presentation will be talked a lot about
such a line segment subtending angle at
a point was kamek lucky so those that we
hope that you have gone through our last
will be so if not we strongly recommend
you take a look at it because that will
help you understand the meaning of java
muse cut they have phrase chord of a
circle subtending an angle at the centre
is come at lucky ayat so now those are
jealous let us understand what this
theorem is really telling us so what it
is telling us since those book chili a
cat in a hammer a circle with centre go
and now what we have done those those we
have actually drawn two quads so you
have a conquer the hey let us say this
is our chord a b and then those were let
us say this is the chord CD so you have
what we have done those though is that
we have drawn two chords and though no
chord actually equal here in length
because homina is a second kid rocky
here now what the theorem is telling us
is age of though equal chords have they
actually subtend equal angles at the
centre of the circle he's commanded
ahead Osaka malam have from last
webisode he chords subtending angle at
the centre of a circle is come mutlar
Kia
so what it means is Agora if you join a
o and Bo Sokolow so you will get this
angle and then similarly if you join Co
and do you will get this angle so those
though the angle subtended by chord a be
at O is this angle there is angle a o be
yay-hay dosto angle subtended by this
chord a be at oh this is angle AOB
similarly those the angle subtended by
chord CD at o is this angle that is
angle C or D so though so the theorem is
telling us the other year don't know
chord they're equal in length is kamala
here that these two angles are equal so
this is what we have to prove this is
what we have to prove so those are now
that we understand the theorem very
clearly equal chords they subtend
equal angle salam ala - Tomika DJ hey
and what is that we have to prove now we
can actually proceed with the actual
proof of the theorem so I can't cut the
head oh so now let us go ahead and prove
this so what we have friends is that
Mary parsec circle have it centered oh
they have drawn two chords a cake or a B
he corner those four chord C D dono
caught on a sec okay draw key here that
these two lengths CD and a B they are
actually equal so hama Malamud also we
have a b is equal to CD this is given
now those though we have to prove that
angle a or b is equal to angle C or D
this is what we have to prove
QK angle subtended by chord a be at O is
this angle similarly angle subtended by
chord
CD at oh is this angle how many honey
have these two angles are equal
now those the app if you look at trying
in triangle a OB and triangle C or D sub
the overall structure is a victim now in
triangles in triangles a a Oh B and C or
D I've noticed each other so that Oh a
is equal to OC o a is equal to OC
alcoholic you because those the Oh a and
OC they are both radius of the same
circle right so they are both basically
our radius similarly the slope OB is
equal to OD so OB is equal to OD again
it is the same reason as above same
reason because OB and OD are again
radius of the same circle right and
those that we know that a B a B is equal
to CD after okay why because this is
actually given to us a be equal to CD
those so these are equal chords which is
given to us so there's no what we are
learning is triangle a o B and triangle
C OD they are actually congruent
triangles they are congruent by they're
congruent by so I am getting a triangle
a o B is congruent to triangle
C or D s / s s s congruence rule that is
side side side you have a a equal to OC
o be equal to OD and a be equal to CD so
those are recall ki J from our series I
think it was series 7j Hebei we were
talking about congruence rules of
triangles so what happened also we have
seen many many congruence rules and we
have proved those congruence rules so
clearly these two triangles are actually
congruent triangles so triangle a OB is
congruent to triangle C or D now maybe
Mohammed Oscar when two triangles are
congruent their corresponding angles and
corresponding sides are equal so that's
the other a B is equal to C D here it's
come at Lepidus code that this angle
should be equal to this circle that is
angle a o B must be equal to angle C OD
Y because these are corresponding parts
of congruent triangles so short form a
Hamas select a hero's though
corresponding parts of congruent
triangles a B K Ulta tariffs angle
heythis and CD k all taker of angle
hedges because a B is equal to C D so
here donor angles are equal and also
this is what we wanted to prove so now
those are chilly a cop got the hell let
us just clean this up and write it in a
way that up jessica exam a test mail
exactly her till it wholly say let us
you know let us write it in that fashion
so as always friends we start with what
is given so we have a circle with centre
o we draw two equal chords say a B and C
D as shown in the figure we join Oh a OB
OC o D right so I'm sure cut the heck
circle case our Java Center here oh then
we actually draw two equal chords EB C D
so by construction basically these two
are equal that is what is given and then
we join Oh a OB OC
od right what's kobato so what do we do
who's khabar have Calcutta here we want
to write a B huh make a proof cornea we
need to prove that angle subtended by
two chords that is angle AOB and angle C
or D they are equal so my proof Kearney
had was know that this angle and this
angle these two angles are equal because
angle subtended by called AV at centre o
is this angle and similarly angle
subtended by God celiac Center oh is
this a girl AHA MIDI honey hey Donald's
angles equal her this is what we have to
prove whose kobato's love what we say
now we actually begin the actual proof
now in triangles a OB a Oh B and C or D
we have Oh a equals OC both are radius
of same circle Oh B equals OD same as
above same argument as a park and a B
equals C D this is given so those the
other hand may 18 oh conditions d ja t
here then what do we have basically we
say that triangle a OB is congruent to
triangle C or D as per sss congruence
rule so it's come at Libya where those
so that if this is equal to this and if
this is equal to this and this is equal
to this then yellow triangle goes though
are congruent triangles as per sss
congruence rule come layer the hero
stuff remark series 7 on triangles aha
way we have learnt about many different
congruence rule scheme so this is sss is
side-side-side this is one of the
congruence rules so those are now every
other no triangles congruent has come at
la vieja dosto it means them that so so
we have a OB is congruent to C or D as
per sss congruence rules therefore angle
AOB this angle is equal to angle C or D
because corresponding angles in
congruent triangles are equal so again
yet on all sides equal here basically is
kamala in case your ulti turn of the
angle here those angles will be up as
maybe are equal
so we say hence it is proved so those
that we hope that you have followed this
theorem proof however there is anything
that you have not understood do not
hesitate to send us a comment or let us
know and we'll be more than happy to
provide further clarification to you so
the sad case presentation made nahi ugly
maybe surveilling a Patrick Alisha Priya
Panama
presentation from rising pearl hum apke
hosaka destroy Aquaman amigos no for
quite some time now we are discussing
series 10 called circles I just already
said number 6 now though so this is the
first theorem on circles that we are
discussing so that's all yeah the
theorem here that states that equal
chords subtend equal angles at the
centre of the circle so also theorem
again is equal chords they subtend equal
angles at the centre of the circle so
those are our chair episode number 6
Atticus waves are malcolm brog botswana
fair Shelia now let us prove why this
theorem is always true so that's the
humming cat of the ham we will just
first we will understand what the
theorem is before we jump into the proof
so if you REM is telling us equal chords
of a circle so equal chords those
pokemon oh my cards come out love hey
Coby the point of letting her circle me
and if you join them by a straight line
okay I'm getting a quad so equal chords
mullah does not make more than one
culture here so equal chords of a circle
they subtend equal angles at the centre
now Kamala Meadows the hamari last
presentation will be talked a lot about
such a line segment subtending angle at
a point was kamek lucky so those that we
hope that you have gone through our last
will be so if not we strongly recommend
you take a look at it because that will
help you understand the meaning of java
muse cut they have phrase chord of a
circle subtending an angle at the centre
is come at lucky ayat so now those are
jealous let us understand what this
theorem is really telling us so what it
is telling us since those book chili a
cat in a hammer a circle with centre go
and now what we have done those those we
have actually drawn two quads so you
have a conquer the hey let us say this
is our chord a b and then those were let
us say this is the chord CD so you have
what we have done those though is that
we have drawn two chords and though no
chord actually equal here in length
because homina is a second kid rocky
here now what the theorem is telling us
is age of though equal chords have they
actually subtend equal angles at the
centre of the circle he's commanded
ahead Osaka malam have from last
webisode he chords subtending angle at
the centre of a circle is come mutlar
Kia
so what it means is Agora if you join a
o and Bo Sokolow so you will get this
angle and then similarly if you join Co
and do you will get this angle so those
though the angle subtended by chord a be
at O is this angle there is angle a o be
yay-hay dosto angle subtended by this
chord a be at oh this is angle AOB
similarly those the angle subtended by
chord CD at o is this angle that is
angle C or D so though so the theorem is
telling us the other year don't know
chord they're equal in length is kamala
here that these two angles are equal so
this is what we have to prove this is
what we have to prove so those are now
that we understand the theorem very
clearly equal chords they subtend
equal angle salam ala - Tomika DJ hey
and what is that we have to prove now we
can actually proceed with the actual
proof of the theorem so I can't cut the
head oh so now let us go ahead and prove
this so what we have friends is that
Mary parsec circle have it centered oh
they have drawn two chords a cake or a B
he corner those four chord C D dono
caught on a sec okay draw key here that
these two lengths CD and a B they are
actually equal so hama Malamud also we
have a b is equal to CD this is given
now those though we have to prove that
angle a or b is equal to angle C or D
this is what we have to prove
QK angle subtended by chord a be at O is
this angle similarly angle subtended by
chord
CD at oh is this angle how many honey
have these two angles are equal
now those the app if you look at trying
in triangle a OB and triangle C or D sub
the overall structure is a victim now in
triangles in triangles a a Oh B and C or
D I've noticed each other so that Oh a
is equal to OC o a is equal to OC
alcoholic you because those the Oh a and
OC they are both radius of the same
circle right so they are both basically
our radius similarly the slope OB is
equal to OD so OB is equal to OD again
it is the same reason as above same
reason because OB and OD are again
radius of the same circle right and
those that we know that a B a B is equal
to CD after okay why because this is
actually given to us a be equal to CD
those so these are equal chords which is
given to us so there's no what we are
learning is triangle a o B and triangle
C OD they are actually congruent
triangles they are congruent by they're
congruent by so I am getting a triangle
a o B is congruent to triangle
C or D s / s s s congruence rule that is
side side side you have a a equal to OC
o be equal to OD and a be equal to CD so
those are recall ki J from our series I
think it was series 7j Hebei we were
talking about congruence rules of
triangles so what happened also we have
seen many many congruence rules and we
have proved those congruence rules so
clearly these two triangles are actually
congruent triangles so triangle a OB is
congruent to triangle C or D now maybe
Mohammed Oscar when two triangles are
congruent their corresponding angles and
corresponding sides are equal so that's
the other a B is equal to C D here it's
come at Lepidus code that this angle
should be equal to this circle that is
angle a o B must be equal to angle C OD
Y because these are corresponding parts
of congruent triangles so short form a
Hamas select a hero's though
corresponding parts of congruent
triangles a B K Ulta tariffs angle
heythis and CD k all taker of angle
hedges because a B is equal to C D so
here donor angles are equal and also
this is what we wanted to prove so now
those are chilly a cop got the hell let
us just clean this up and write it in a
way that up jessica exam a test mail
exactly her till it wholly say let us
you know let us write it in that fashion
so as always friends we start with what
is given so we have a circle with centre
o we draw two equal chords say a B and C
D as shown in the figure we join Oh a OB
OC o D right so I'm sure cut the heck
circle case our Java Center here oh then
we actually draw two equal chords EB C D
so by construction basically these two
are equal that is what is given and then
we join Oh a OB OC
od right what's kobato so what do we do
who's khabar have Calcutta here we want
to write a B huh make a proof cornea we
need to prove that angle subtended by
two chords that is angle AOB and angle C
or D they are equal so my proof Kearney
had was know that this angle and this
angle these two angles are equal because
angle subtended by called AV at centre o
is this angle and similarly angle
subtended by God celiac Center oh is
this a girl AHA MIDI honey hey Donald's
angles equal her this is what we have to
prove whose kobato's love what we say
now we actually begin the actual proof
now in triangles a OB a Oh B and C or D
we have Oh a equals OC both are radius
of same circle Oh B equals OD same as
above same argument as a park and a B
equals C D this is given so those the
other hand may 18 oh conditions d ja t
here then what do we have basically we
say that triangle a OB is congruent to
triangle C or D as per sss congruence
rule so it's come at Libya where those
so that if this is equal to this and if
this is equal to this and this is equal
to this then yellow triangle goes though
are congruent triangles as per sss
congruence rule come layer the hero
stuff remark series 7 on triangles aha
way we have learnt about many different
congruence rule scheme so this is sss is
side-side-side this is one of the
congruence rules so those are now every
other no triangles congruent has come at
la vieja dosto it means them that so so
we have a OB is congruent to C or D as
per sss congruence rules therefore angle
AOB this angle is equal to angle C or D
because corresponding angles in
congruent triangles are equal so again
yet on all sides equal here basically is
kamala in case your ulti turn of the
angle here those angles will be up as
maybe are equal
so we say hence it is proved so those
that we hope that you have followed this
theorem proof however there is anything
that you have not understood do not
hesitate to send us a comment or let us
know and we'll be more than happy to
provide further clarification to you so
the sad case presentation made nahi ugly
maybe surveilling a Patrick Alisha Priya
Panama
About this Video
Sep 20, 2025
Last updated
Related Exams
Equal chords subtend equal angles at the center of a circle (Theorem and proof) for Class 92025 is part of Class 9 preparation. The notes and questions for Equal chords subtend equal angles at the center of a circle (Theorem and proof)
have been prepared according to the Class 9 exam syllabus. Information about Equal chords subtend equal angles at the center of a circle (Theorem and proof) covers all important topics
for Class 92025 Exam. Find important definitions, questions, notes, meanings, examples, exercises
and tests below for Equal chords subtend equal angles at the center of a circle (Theorem and proof).
Introduction of Equal chords subtend equal angles at the center of a circle (Theorem and proof) in English is available as part of our Class 9 preparation & Equal chords subtend equal angles at the center of a circle (Theorem and proof) in Hindi
for Class 9 courses. Download more important topics, notes, lectures and mock test series for Class 9 Exam by
signing up for free.
Description
Video Lecture & Questions for Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9 - Class 9 full syllabus preparation | Free video for Class 9 exam.
Information about Equal chords subtend equal angles at the center of a circle (Theorem and proof)
Here you can find the Equal chords subtend equal angles at the center of a circle (Theorem and proof) defined & explained in the simplest way possible. Besides explaining types of Equal chords subtend equal angles at the center of a circle (Theorem and proof)
theory, EduRev gives you an ample number of questions to practice Equal chords subtend equal angles at the center of a circle (Theorem and proof) tests, examples and also practice Class 9 tests.
Related Searches
ppt
,video lectures
,Important questions
,shortcuts and tricks
,study material
,Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9
,Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9
,Semester Notes
,Exam
,Summary
,Free
,past year papers
,practice quizzes
,Previous Year Questions with Solutions
,Objective type Questions
,MCQs
,Sample Paper
,mock tests for examination
,Equal chords subtend equal angles at the center of a circle (Theorem and proof) Video Lecture - Class 9
,Viva Questions
,Extra Questions
;
Study Equal chords subtend equal angles at the center of a circle (Theorem and proof) on the App
Students of Class 9 can study Equal chords subtend equal angles at the center of a circle (Theorem and proof) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Equal chords subtend equal angles at the center of a circle (Theorem and proof),
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Equal chords subtend equal angles at the center of a circle (Theorem and proof) is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup