Angles in semi-circle are always 90 - Theorem Video Lecture - Class 9

hello those so welcome welcome to this
presentation from rising pearl
hum apke hosiah destroy and friends
today we are talking about CDs 10 jaha
combat kavaja circles key RJ webisode
number 18
those two item yet here improve carnage
IRA had that says circle or angle in a
semi-circle is a right angle
so is the angle in a semi-circle is a
right angle right angle comma Club have
kamalu a right angle is 90 degrees so
the theorem is telling us the co every
angle in a semi-circle must be always 90
degrees so this is a typical Agatha hey
how we can prove this theorem so iam
Calcutta have friends we have actually
drawn a circle with Center oh so now
next what we want to do those two is
this a V hum yabai we want to draw a
diameter a B AB Kamala Medusa what is a
diameter diameter is basically so yeah
your a B hey friends this is a diameter
now diameter is nothing but it is any
cord that passes right through the
center of the circle so those are now
Jacobi have diameter draw can't they
hole up Kamala it actually divides a
circle into two equal parts so aka upper
valley part or equal here bottom body
part on each of these parts go home cat
ahead semicircle say Mika MATLAB aha
same ago Matt lepay half right because
diameter circle Co equally though part
may divide country here basically hummed
each of the half go home Cathy
semicircle sorry America's Doh
semicircle head so those are now other
up you jo-jo a bottom part or your
bottom semicircle higher up is a base
little if you think this to be the base
right then those two up other upper body
part me if you randomly take any point
so I can cut the head of such Ellie let
us let us actually take a point so you
have to go
we have taken a point P so edge from the
Point Pelee heroes that we have taken
any point on the top half of the
semicircle so those are then jab Hum
when we join AP and BP so yeah angle one
three heroes to this angle you say hum
cat the head angle in a semicircle now
come on amigo so basically I think it
was our episode number 16 that is da
webisode ballet thumbnail egg puri
webisode we have talked about key angle
subtended by an arc inside a circle
whose comic lucky hair so you're happy
goes to basically what we are saying is
Yaya Marie semicircle and each over the
a be a semicircle it basically subtends
this angle a P B at Point P so a Johari
angle a a PBE angle Hadassah is super
valley semicircle may this is an angle
in a semi-circle a bit theorem is
telling us key angle in a semi-circle
must be right angle is come at levodopa
the theorem is telling us that hamari
goj angle e p behead this angle must
always be himesh a measure this must be
a right angle triangle it must be 90
degrees this angle should be 90 degrees
similarly goes to man leisure come
country let us take one other point
Shelley I be randomly HMDA we have taken
another point Q in the semicircle so i
videos though what is the angle
subtended by this a B at Point Q it is
this angle so again those the a QB is
angle in a semicircle so by theorem
again this must be equal to 90 degrees
so this is what the theorem is telling
us away abso chögyam Jabba Jabba
diameter draw currently ho
then both upper body part or Nature
Valley part oh no he semicircle he right
so hum make you nietzsche velichko
baseband i had so those icy but nahi had
that you have to always make the bottom
up
at your base so it can cut the head off
so let us reverse this now you have a
break okay those two what we have done
is that hum Niobe we have actually made
the top semicircle as our base or have
never Nietzsche Valley semicircle may we
have taken teen point P Q and R so the
study each of these angles here angle
APB a valley angle angle a q be a valley
angle and similarly angle a are B that
is this angle
Yeti no kitty no angle those though they
are all angles in a semi-circle and
according to the theorem each of these
should be 90 degrees this come at the
head a PB should be 90 degrees is comic
love hair a QB should be 90 degrees and
it's comical ahead a are B should be 90
degrees so those four we hope that
theorem calculator here yet it is very
clear to us right now
eventually potala gotta hey how we can
prove this theorem so those are like we
always do eventually let us start out
systematically so how make adiga here we
have a circle with centre o as shown in
the figure
simple CX our color we have a center oh
right away those so now next we see that
now how may prove Kearney had at any
angle in a semicircle is a right angle
yeah something that we have to prove so
hum Calcutta halos though we draw a
diameter as shown in the figure then we
take any point p on the circle and join
AP and BP so how make diameter a bead a
seeker k join come to here we draw a
diameter a b and then randomly we take
any point p p point Lineker bath
we actually join a p and b
we join them like this so together so
now next what do we do
arre those though we we note that now
yeah hamari semi-circle handy J a B so
this semicircle actually subtends this
angle at the center right and similarly
eh a semicircle here G some day bold
white my highlight key here that
subtends this angle at any other point
outside the outside this arc right but
look a gap you take the arc a B this arc
subtends angle a o be at the center and
the same arc subtends angle a PB
anywhere outside the arc a B so though
so then from theorem have a Madame Han
that years your angle here will be two
times this angle yet theorem those that
we have actually proved about the
webisode spelling right so we know that
angle subtended by any arc at the center
of the circle is double or two times the
angle subtended by the arc anywhere else
on the circle so from here those that we
know that a OB is two times a PB right I
mean next goes though what do we know
amigos the a OB is equal to 180 degrees
right Q Y is a OB 180 degrees well
because a OB is a straight line QK the
diameter X is a straight line this
cometh none of this angle is 180 degrees
so other those though now if a OB is
equal to nine if it is equal to 180
degree or Joe APB here that is half of a
OB then what do we get so it's come at
the via who are those though Joe a OB
here which is two times a PB so two
times a PB is equal to a or b or two
times a PB hey 180 degree so the
monocyte cover-up to say divide that
they have
P is equal to 180 degree by two which is
equal to 90 degree so I am Radhika those
though even though we have taken any
random point p on the circle we have
proved that a Joha a PB this angle is 90
degrees and hence we say the theorem is
proved so some Asha cut the hair you
have followed the theorem other argument
may go it out here if you have any
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