A circle is a simple closed shape defined as the set of points equidistant from a central point, with key components including radius, diameter, sector, chord, arc, circumference, segment, and semicircle. The diameter connects two points on the circle and is the longest chord, while other terms like arc and sector define specific parts and areas within the circle. The document outlines properties and mathematical definitions essential for understanding circles in geometry.

1. CIRCLES

2. What are Circles
?A circle is a simple
closed 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.

3. PARTS
OF A
CIRCLE
1.Radius
2.Diameter
3.Sector
4.Chord
5.Arc
6.Circumference
7.Segment
8.Semicircle

4. RADIUS OF A
CIRCLE

5. In geometry, a diameterof a circle is any straight linesegmentthatpasses through the center of
the circle and whose endpoints lieon the circle. It can also be defined as the longest chord of
thecircle. Both definitionsare also validfor the diameter of a sphere. The word "diameter"is
derived from Greek διάμετρος (diametros), "diameter of a circle", from δια-(dia-), "across,
through" + μέτρον (metron), "measure".[1] It is often abbreviated DIA, dia, d, or ⌀.Inmore
modern usage, thelengthof a diameteris also called thediameter. Inthissense one speaks
of thediameterrather than adiameter (which refers to thelineitself),because all diameters of a
circle or sphere have the same length,thisbeing twice the radius r.

6. SECT
OR
OF
A
CIRCL
A circular sector or circle
sector (symbol: ⌔), is the
portion of a disk enclosed by
two radii and an arc, where
the smaller area is known as
the minor sector and the
larger being the major sector.
In the diagram, θ is the central
angle in radians, {displaystyle
r} r the radius of the circle,
and {displaystyle L} L is the

7. CHO
RD
OF
A
A chordof a circleis a straight line
segment whose endpoints both lie
on the circle. A secant line, or
just secant, is the infiniteline
extension of a chord. More
generally, a chord is a line segment
joining two points on any curve,
for instancean ellipse. A chord that
passes through a circle's center
point isthe circle's diameter .The
word chordisfrom
theLatin chorda meaning bowstri
ng.

8. AR
In Euclidean geometry, an arc (symbol: ⌒) is a closed segment of
a differentiable curve. A common example in the plane (a two-dimensional manifold), is
a segment of a circle called a circular arc.[1] In space, if the arc is part of a great
circle (or great ellipse), it is called a great arc.
Every pair of distinct points on a circle determines two arcs. If the two points are not
directly opposite each other, one of these arcs, the minor arc, will subtend an angle at
the centre of the circle that is less than π radians (180 degrees), and the other arc,
the major arc, will subtend an angle greater than π radians.

9. The circumference (from Latin circumferentia, meaning "carrying
around") of a closed curve or circular object is the linear distance
around its edge. The circumference of a circle is of special
importance in geometry and trigonometry. Informally
"circumference" may also refer to the edge itself rather than to the
length of the edge. Circumference is a special case of perimeter:
the perimeter is the length around any closed figure, but
conventionally "perimeter" is typically used in reference to
a polygon while "circumference" typically refers to a continuously
differentiable curve.
Circumference
Of
A
Circle

10. SEGMENT
OF A
CIRCLE
In geometry, a circular segment (symbol: ⌓) is a region of a circle which is
"cut off" from the rest of the circle by a secant or a chord. More formally, a
circular segment is a region of two-dimensional space that is bounded by
an arc (of less than 180°) of a circle and by the chord connecting the
endpoints of the arc. The area formula can be used in calculating the volume
of a partially-filled cylindrical tank.In the design of windows or doors with
rounded tops, c and h may be the only known values and can be used to
calculate R for the draftsman's compass setting.

11. SEMICIRCLE
In mathematics (and more specifically geometry), a semicircle is a one-
dimensional locus of points that forms half of a circle. The full arc of a
semicircle always measures 180° (equivalently, π radians, ora half-
turn). It has only oneline ofsymmetry (reflection symmetry). In non-
technical usage, the term "semicircle" is sometimes used to refer to a
half-disk, which is a two-dimensional geometric shape that also
includes the diameter segment from one endof the arcto the otheras
well as all the interior points.
By Thales' theorem, any triangle inscribed in a semicircle with a vertex at
each of the endpoints of the semicircleand the third vertex elsewhere
on the semicircle is a right triangle, with right angle at the third vertex.

12. #THANK YOU
PRESENTED BY-BHAVESH
SINGH