Circles are geometric figures whose points all lie the same fixed distance from a central point called the center. A circle is defined as the collection of all points in a plane that are equidistant from a fixed point. The line segment from the center to any point on the circle is called the radius, and the longest possible chord that passes through the center is the diameter, which has a length twice that of the radius. Circles have key properties like circumference, arcs, segments, and sectors that are defined in the document. Formulas are also provided relating circumference, diameter, radius, area of circles and circular segments.

1. CIRCLES
1

2. WHAT ARE CIRCLES?
 The collection of all the points in a plane
which are at a fixed distance from a fixed
point in a plane , is called a CIRCLE.

3. REMARKs-
1.The line segment joining the
center and any point on the circle
is also called a RADIUS of the
circle.

4. 2.DIAMETER is the longest chord and all
diameters have the same length which is
equal to two times the radius.

5. 3.A piece of a circle between two points is called
an ARC.

6. REMARKs-
4.The length of the complete circle is
called its
CIRCUMFERENCE.

7. 5.The region between a chord and either of
its arcs is called a SEGMENT of circular region
or simply a segment of the circle.

8. REMARKS-
6.There are two major types of
segments , which are the MAJOR
SECTOR and the MINOR SECTOR.

9. 7.The bigger one is
called the MAJOR
SECTOR and the
smaller one is known as
MINOR SECTOR.

10. RELATION BETWEEN
CIRCUMFERENCE AND
DIAMETER
CIRCUMFERENCE = 3 x
DIAMETER(APPROX))
Diameter

11. CIRCLES-
Another prevalent kind of simple closed
curve is a circle. Circles are geometric
figures whose points all lie the same
distance from a given point, the circle's
center.They are not polygons, because
they are not made up of segments.
Points that lie in the same line, like those
in a segment, are never equidistant (an

12. FORMULA’S OF
CIRCLES-1*Diameter = 2 x radius of circle
2*Area of Circle:
area = PI r2
3* Circumference of Circle = PI x diameter = 2 PI x radius
where PI = PI = 3.141592...
4* Length of a Circular Arc: (with central angle theta).
if the angle theta is in degrees, then length = theta x
(PI/180) x r
if the angle theta is in radians, then length = r x theta

13. FORMULA’S OF
CIRCLES-5* Area of Circle Sector: (with central angle theta)
if the angle theta is in degrees, then area =
(theta/360)x PI r2
if the angle theta is in radians, then area =
((theta/(2PI))x PI r2

14. THANKYOUNAME- Karan Singh
Rawat
CLASS-9TH
SECTION-A
D.C.MODEL SR. SEC.
SCHOOL