Number of Tangents from a Point to a Circle Video Lecture | Crash Course: Class 10

hello friends welcome to rising pearl
calm today we're talking about series 10
where we're learning or creating on
circles this is ever so number 10 and
since today we will talk about how many
tangents can be drawn from an external
point to a circle this webisode I must
tell you at the beginning is more
conceptual in nature because we want to
make sure that you understand all
aspects of circle and tangents so let's
get started so what we are going to do
is we are going to first stake any point
which is on the circle so here what we
have done we have a circle with Center o
this is the circle and let's take any
point let's call this point E and I have
drawn a line passing through a now how
many other types of lines can I draw so
I can draw another line like this this
this this this this so in other words
friends you will notice that I can draw
I can actually draw in finite number of
lines that passes through point a right
but you will notice that there is only
one line which is this line which is
this line that actually touches a circle
only at one point each in every of the
other line for example if you look at
this line this line this line and all
other lines they will intersect the
circle in at least two points so one
point obviously is a the other point for
this line is this this is the other
point for this line this is the second
point for this line this is the second
point so in other words each and every
of the lines except for this line let's
see if can highlight this line all other
lines so let's see if we can highlight
this yeah so all the other lights except
the bright yellow line they intersect a
circle at two points so they are all
seconds of the circle but yellow line
there is only one tangent so only one
tangent for a point on the circle that
is if you take a particular point on the
circle you can draw
only one tangent that passes through
that point you cannot write any more
tangents now this time let's take a
point which is inside of a circle this
time we have taken a point this time
this is a point a but this endpoint is
actually inside the circle this is
inside the circle now let's draw some
lines that passes through point a and
these are some of the lines that I have
drawn which are passing through pointed
as you can see each of these lines they
actually intersect the circle in two
points all of them that means you cannot
draw even one single line that touches a
circle at only one point each and every
of the lines that passes through point E
will intersect the circle at two points
so there are no tangents so there are
zero tangents you cannot draw any
tangent from a point which is already
inside a circle so zero tangent now this
time we will go and try to take a point
which is outside our circle so this is a
circle this is a point a which is
outside the circle it is not on the
circle it is not inside the circle it is
outside the circle now you can draw all
of these lives so here I have drawn all
these lines you will notice that there
is only there are only two lines
highlighted by bright yellow over here
where the the straight lines touch the
circle at only one point here and here
for these lines these other lines so
let's say these three lines that I have
shown let's call them l1 l2 and l3 so l1
l2 and l3 are basically the non
intersecting lines right they are non
intersecting lines how about these lines
let's call these lines these lines m1 M
- and m3 so these lines m1 m2 m3 are
seconds of the circle they intersect a
circle at two points so this for m1
these are the two points for m2 these
are the two points for m3 these are the
two points but these bright yellow lines
are the only two lines with the straight
line touches a circle at only one point
and these are the points respectively
it means that if you take any external
point from there you can draw two
tangents not one not three only two
tangents can be drawn from any one
external point to any given circle so
friends in the next webisode we have to
take a look at what can we what can we
know about these two tangents which are
drawn from same external point to a
common circle