01 - Introduction to Circles - Class 10 - Maths Video Lecture

hey friends you can see various pictures
and figures on the screen did you notice
anything common between them all the
above things look similar to a
particular shape that is a circle for
example the shape of a bangle shape of a
pizza bicycle wheel coins etc circle is
one of the most common shapes in this
universe in this session we will learn
all the basic terminologies in context
to a circle let me take you to a park
which is nearby my house which is also
round and this park has some special
features which we learn throughout this
session firstly there is a fountain
exactly in the center of the park and
benches are put around the boundary of
the park here you can see that the park
is a circle and the fountain is in the
center of the circle and the benches are
on the boundary of the park which is
equidistant from the fountain
mathematical definition of circle is
also on the same lines a circle can be
defined as the collection of all the
points in a plane which are at a fixed
distance from a fixed point in the plane
the fixed point is called the origin of
the circle and the fixed distance is
called as the radius if you see there is
a path which connects the fountain and
the entrance gate this path can be
called as the radius the radius is the
distance from the center of the circle
to the boundary of the circle radius is
a Latin word which means the way or the
spoke of a wheel radius is denoted by a
small letter R
now if we extend that path to meet the
other side of the boundary of the park
passing through the fountain then it
will be called as a diameter the
diameter of the circle is a straight
line passing through the center
connecting two points on the boundary of
the circle diameter comes from a Greek
word diameter oz where dye means across
or through and metrons
means to measure diameter is denoted by
the small letter D as you can see that
diameter touches the circle at two
different points
well then any line segment which touches
the circle at two different points it is
known as a chord of the circle god of a
circle is a straight line connecting two
points on the circle where it is visible
in the path that diameter is the longest
chord in the park now if the same road
extends on both the sides outside the
park then that road can be called as a
secant of the park c-care in Latin means
to cut and hence any line which cuts the
circle is called as a secant kindly note
the difference between diameter cord and
a secant donítö is a cord which passes
through the center whereas cord touches
at any two points on the circle and
secant is a line stretching to infinity
at both the directions now once we have
drawn a chord or a segment we can see
that the park gets divided into two
regions
now these regions are known as segments
the segment of the circle is the region
bounded by a chord and the arc subtended
by the chord the larger area is known as
major segment and the smaller one is
known as a minor segment if the chord or
a secant is a diameter then the circle
gets divided into two equal regions and
in our case it gets divided into two
equal semi circles now just imagine if
you're jogging around the boundary of
the park and when you complete one round
of this boundary it is known as the
circumference of this circular Park in
which you're jogging circumference is
the distance around the boundary of a
circle if you noticed the road in front
of the park touches the park only at the
entrance gate of the park so if there is
a line which touches the circle at one
and only one point then it will be
called as a tangent to the circle
however they can be infinite lines that
can be drawn to a point on the circle
but there is only one line that touches
the circle through that point on the
boundary of the park there is a part
which contains all type of flowers this
area is just a small part of the
boundary and you can see that it looks
like an arc and so friends is called as
an arc itself an arc is the portion of
the boundary or the circumference in the
circle now we saw the area which is
flowers there are two ways to go to that
area but both the paths start from the
fountain
if we concentrate only on that
particular area it will be called as a
sector of a circle sector of a circle is
the area bounded by two radii and an arc
subtended between them now actually have
understood what a sector is so can you
give me some another example for sector
I'll give you a hint we all love pizza
one particular slice of pizza can be
called as a sector the smaller region is
known as - sector and the bigger region
is known as a major sector kindly note
the difference between sectors and
segments sectors and segments both are
bounded by an arc but the difference is
that sectors are enclosed by two radii
and segments are enclosed by a code and
when that code is a diameter sectors are
equal to segments let us quickly recall
what all we have learnt in this session
so friends before we end this session
let me just ask you one last question do
you think earth is also a circle the
answer is no Earth is not a circle do
not confuse the shape of Earth with a
circle or a spherical in shape and three
dimensional in nature whereas a circle
is a two dimensional shape in a single
plane that's all for this session in the
next session we will learn something
more on a tangent to a circle if you
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