L9 : Angle subtended by arc - Circles , Maths, Class 9 Video Lecture

hello friends this video encircles part
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more fear from example let's try to find
a relationship between God and Ark we do
an activity so you can also do that take
a piece of paper pen compass and the
whole zoetry said and in this circle
first 2 also good drawer to e for
thoughts okay and not miss it haha and
in this card be happy until it ok now I
can do one thing
so now I ad still to CP is the card we
have created we have drawn that is
Becca's affection so we will observe
that these are the minor of a V will be
equal to minus E in fact what you can
superimpose you can actually cut the
piece of paper you can cut this cut this
arc CD and you see that you can actually
superimpose what part on each other
thus we conclude that the equal God
makes concrete that is a conclusion by
this activity and the converse is also
true
okay now let's understand the angle
subtended by arc of a circle we have
seen the half of the circle and let's
see what is the concept of the angle
subtended by it so I know subtended by
car so in this case I talk about - ah Oh
mr. Buddha Tom
so angle subjected by the minor arc and
the center is defined and acquired and
your subject by the corresponding chord
so if you see here if he was the point
so when you say I know submitted by arc
a B or angle subtended by God may be
both are seeing both uptrend to see -
thank you Tom so if you have take two
point TV so we talked about angle
subtended by the start and talk about
angle subtended by this court both are C
minus
by the God and the angle subtended by
the same arc corresponding on with the
same thing
hey what was morning - odd so I guess is
that angle separated by a minor are at
the center of a circle is defined as
nothing but angle subtended by
corresponding God does it okay
you see minor arc subtends an angle e OB
but if you don't put a major arc that
point Dixie here
so I guess subtended by this major arc
is nothing but the place I come the
reflex angle what angle subtended by the
minor arc is nothing but angle viewing
angle subtended by God is also same
without see I got separated by God a B
is equal to angle seven PI minus R maybe
I got separated by the major are a be
something but the reflects on the right
okay there's a very positive M let's
understand this will have lot of
numerical speech with sure the QM says
that the angle subtended by an arc at
the center of the circle is twice or is
double the angle subtended the buyer it
at any other point on the surface
example this is angle let's say let me
say what they want to say so this is
might be human and they want to say that
angle P Q is equal to twice that is what
they want to see the sign will be Q will
be equal to twice angle p eq under
subtended by an arc at the center that
is like a P Q is equal to double the
angle subtended by the same arc and any
other
the circumcircle very very important
theorem let's try to do it to do this
let's join this view okay and it's
number these triangles so we had to
prove that and the P or Q is equal to
twice of angle p AQ or i can say that
yogi is what I get for plus angle B is
equal to twice off okay so let's see see
in this triangle a Opie a movie he
always will do you radius what's hip
side
therefore I just
similarly in triangle a q EO q AO will
be equal to okay therefore U is equal to
what I will be equal that is negative
one is these two equation me a party
okay so now my let's see is the same
triangle a triangle a o P angle is Phi
is one so the angle for and therefore is
the exterior angle and that is equal to
sum of the opposite angle that is equal
to 85 Plus night at 6:00 okay and I can
see that this is nothing but angle five
is what I got six anger 6 plus 906 that
is nothing but twice 806 similarly
triangle a huge you see and the three
exterior angles are the worst of all oh
my god that is like a one as
we have to write that set the form find
the one so I can say I get one plus the
angle one why because I got two is equal
to make it one why so Magdeburg you add
these two equation this is the equation
three and equation 4 add these two
equation you add these two equation
again but twice the angle 6 plus twice
cycle and that is what we have to okay
very very important theorem is by I and
the center is double the angle subtended
by the same arc and any other parts of
our the theorem derive from this
interesting theorem angle subtended by
same segment of circle are equal that
means if you see V is the segment this
will subtend same angle on the minor arc
angle one is by doing it correctly so
they're there to Point C V it will
separate C - you take another angle also
here it will be same so we can easily
prove that C angle 1 is what angle 3 by
2 correct angular this is half Omega 3
I'm going to use work in half of a go
through the theorem which we shall it is
not correct so you see you put the side
with our is the same there what I got is
very pretty easy angle in the same
segment of the circular ring
let's take another important element say
that the angle subtended by an arc of a
circle angles up and go to the same
circle with the right angle so if
there's a tie me down here you get the
same circle you find this angle will be
like right so we know that angle b RQ is
one-half of angle P this is like because
angle subtended by same arc at the
center is twice I guess filled by the
Sigma I'd be the point
what is I'm going to be you want it
straight line it up and this is my
previously that they can be a Q is 90
degrees so question was it the line
segment joining two points that is two
point we either they subtend equal I
collect other dew points and it was
point B C and this balcony
so given that angle 1 is equal to ever -
okay line segment joining the point
where you enjoy you know so if you want
the line segment going to find this
obtained equal and this that it need
every point it is something like this
and this to Evie points obtains
equal angle X evening right so we have
to prove that all these four points are
like honest angles we have to prove this
so what we can do with this doll circle
and again just assume that assume that D
is not lying on us
or other server okay it is given that
angle 1 is equal to Ingrid
okay now onyx stick appoint me same
please
hey and let this be n 2 3 this is by
construction hang Cavanaugh's can do
anything by like you know right because
they are destroying your another point
here e the same eb and we can see that
thank you the month or equal to n 2 3 pi
rule just understand if this is possible
we need D and G coincide right and then
I can say that the assumption that he is
not lying on the circle circle is wrong
correct that means all these for ponding
in the circle also directly you can say
that if this is given angle 1 is good to
anchor to be given this is the case of I
mean this is the case when all these
points lie on the circle then I can say
that if these two are nothing but point
you should make yourself like this they
can say that this converse of that okay
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