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CIRCLES
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.
PARTS
OF A
CIRCLE
1.Radius
2.Diameter
3.Sector
4.Chord
5.Arc
6.Circumference
7.Segment
8.Semicircle
RADIUS OF A
CIRCLE
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.
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
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.
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.
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
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.
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.
#THANK YOU
PRESENTED BY-BHAVESH
SINGH

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Circles - An Introduction

  • 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.
  • 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.