Areas related to circles For Class 10th

1. Areas related to circle

2. Circles
 A circle is a simple shape in Euclidean geometry. It is the set of
all points in a plane that are at a given distance from a given point,
the centre; equivalently it is the curve traced out by a point that moves
so that its distance from a given point is constant. The distance between
any of the points and the centre is called the radius.
 A circle is a simple closed curve which divides the plane into two
regions: an interior and an exterior. In everyday use, the term "circle"
may be used interchangeably to refer to either the boundary of the
figure, or to the whole figure including its interior; in strict technical
usage, the circle is only the boundary and the whole figure is called
a disk.

3. A circle with circumference (C) in
black, diameter (D) in Blue, radius
(R) in red, and centre (O) in
magenta.

4. Parts of Circle
 Arc: any connected part of the circle.
 Centre: the point equidistant from the points on the circle.
 Chord: a line segment whose endpoints lie on the circle.
 Circumference: the length of one circuit along the circle, or the distance
around the circle.
 Diameter: a line segment whose endpoints lie on the circle and which passes
through the centre; or the length of such a line segment, which is the largest
distance between any two points on the circle. It is a special case of a chord,
namely the longest chord, and it is twice the radius.
 Segment: a region, not containing the centre, bounded by a chord and an arc
lying between the chord's endpoints.
 Radius: a line segment joining the centre of the circle to any point on the circle
itself; or the length of such a segment, which is half a diameter.

5. Chord, secant, tangent,
radius, and diameter
Arc, sector, and segment

6. Length of
Circumference The ratio of a circle's circumference to its diameter is π (pi),
an irrational constant approximately equal to 3.141592654. Thus
the length of the circumference C is related to the radius r and
diameter d by:
C=2πr

7. Area of the Circle
 As proved by Archimedes, the area enclosed by a circle is equal to
that of a triangle whose base has the length of the circle's
circumference and whose height equals the circle's radius,[7] which
comes to π multiplied by the radius squared
Area=πr2

8. Areas of Combination of Plane Figures
Acollection of points that are on a plane is
known as a plane figure.

9. Summary
Circumference of a circle = 2πr
Area of a Circle = πr2
Area of a segment of a circle
= Area of a corresponding sector –
Area of a corresponding triangle

10. Made by Muhommad Zubair
Class Xth A
Roll No 27 (twenty seven)