The Basic Vocabulary and Rules of Circles. Conic Sections: Circles. Circles: The Basics and Definitions, Including Radius. The Area of a Circle. Tangents to Circles. Graphing Circles. Circles PowerPoint. Circumference and Area of a Circle. Examples of How to Find the Areas of Circles. Finding the Areas of Circles. Fundamentals of Geometric. Starter: Problem solving task to calculate the area of a pattern involving squares and quarter circles. Main: Animated examples (using the MORPH PowerPoint transition) of splitting the circle into sectors to form a rectangle and derive the formula for the area (Could be used as an activity - see extra below). PowerPoint Presentation. Area of Circles. Return to table. of contents. Area of a Circle The Area (A) of a Circle is found by solving the following formula: 7 cm Find the area of the circle. A = π r2 1. Substitute the radius into formula. A = π (7)2 2. Use 3.14 as an approximation for π. Area & Perimeter By, Jennifer Sagendorf ITRT – Suffolk Public Schools Perimeter of a Rectangle To calculate the perimeter of an object or space, you will need to add the length and width, then multiply by 2. (2 + 4) x 2 = _____ It means the same as: (2 + 4) + (2 + 4) = _____ Try to find the perimeter of these rectangles. Perimeter of a.

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## Perimeter and Area - PowerPoint PPT Presentation

The Circle Monday 4 June 20121. Know the names of a circle’s features2. Calculate the circumference3. Calculate an arc length4. Deal w Start on. Show related SlideShares at end. WordPress Shortcode. Link. Area of circle ppt. 23,085 views. Share. Like. Download. kirdash99. Follow. Published on Jun 3, 2012. Published in: Spiritual, Education. Download our 100% free Circular templates to help you create killer PowerPoint presentations that will blow your audience away. For privacy reasons Facebook needs your permission to be loaded. For more details, please see our Privacy Policy.

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The Circle. Learning Objective: To find the circumference and area of a circle. Circumference. Circumference = π × diameter. diameter. circumference. Area. Area of a Circle. Geometry 10/30/2013. Fraction Circles worksheet. Notice the different lines Embedded in the circle. Activity. Cut the circle along the solid. Find the area of each figure. Give exact answers, using if necessary. 1. a square in which s = 4 m. 2. a circle in which r = 2 ft. 3. ABC with vertices A(–3, 1), B(2.

Apr 27, 2009 — This is the "Area of Circle" Maths Presentation. It is one of the Top Three pieces of Homework I've done. It's as easy as pi. Let's first make sure that we understand the difference between circumference and area. The circumference of a circle is the perimeter of the.

### Area of a circle calculator

Circle - Wikipedia

## Circle

Circle | |
---|---|

A circle (black), which is measured by its circumference ( C), diameter (D) in circlee, and radius (R) in red; its centre (O) is in magenta. |

A **circle** is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it or the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.

Specifically, a circle is a simple closed curve that 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 pph the boundary and the whole figure is called a disc.

A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus or variations.

### Euclid's definition

A circle is a plane figure bounded by qrea curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.

### Topological definition

In the field of topology, a circle isn't limited cicle the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of **R**^{3} upon itself (known as an ambient isotopy).^{[2]}

### Terminology

- Annulus: a ring-shaped object, plt region bounded by two concentric circles.
- Arc: any connected part of a circle. Specifying two end circle of an arc and a center allows for ;pt arcs that together make up a full circle.
- Centre: the point equidistant from all points on the circle.
- Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments.
- 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 that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a ot, namely the longest chord learn more here a given circle, and its length is twice the length of a radius.
- Disc: the region of the plane bounded by a circle.
- Lens: the region common to (the intersection of) two overlapping discs.
- Passant: a coplanar straight line that has no point in common with the circle.
- Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter.
- Sector: a region bounded by two radii of equal length with a common center and either of the two possible arcs, determined by this center and the endpoints of the radii.
- Segment: om region bounded by a chord and one of the arcs connecting the chord's endpoints. The length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term
*segment*is used only for regions not containing the center of the circle to which their arc belongs to. - Secant: an extended chord, a coplanar straight line, intersecting a circle in two points.
- Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as center. In non-technical common usage it may mean the interior of the two dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case ob a segment, namely the largest one.
- Tangent: a coplanar straight line that has one single point in common with a circle ("touches the circle at this point").

All of the specified regions may be considered as *open*, that is, not containing their boundaries, or as *closed*, including their respective boundaries.

Chord, secant, tangent, radius, and diameter |

### History

The word *circle* cirrcle from the Greek κίρκος/κύκλος (*kirkos/kuklos*), itself a metathesis of the Homeric Greek κρίκος (*krikos*), meaning "hoop" or "ring".^{[3]} The origins of the words *circus* and *circuit* are closely related.

The circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, Sun, and a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand. The circle disney nds nintendo ds er the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study curcle the circle has helped inspire the development of geometry, astronomy and calculus, area.

Early science, particularly geometry and astrology and astronomy, was connected to avg antivirus edition 2012 divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.^{[4]}^{[5]}

Some highlights in the history of the circle are:

- 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 (3.16049.) as an approximate value of π.
^{[6]}

### Analytic results

### Circumference

The ratio of pph circle's circumference to its diameter is π (pi), an irrationalconstant approximately equal to 3.141592654. Thus the circumference *C* is related to the radius *r* and diameter *d* by:

### Area enclosed

As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is srea to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius,^{[8]} which comes to π multiplied by the radius squared:

Equivalently, denoting diameter by *d*,

that cirvle, approximately 79% of the circumscribing square (whose side is of length *d*).

The circle is the plane curve enclosing the maximum area for a given arc length. This relates cricle circle to a problem in the calculus of variations, namely the ppg inequality.

### Equations

#### Cartesian coordinates

*r*= 1, centre (

*a*,

*b*) = (1.2, −0.5)

**Equation of a circle**

In an *x*–*y*Cartesian coordinate system, the circle with corcle coordinates (*a*, *b*) and radius *r* is the set of all points (*x*, *y*) cigcle that

This equation, known as the Equation of the Circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right-angled triangle whose other sides are of length |*x* − oj and |*y* − *b*|. If the circle is centred at the origin (0, 0), then the equation simplifies are

**Parametric form **

The equation can be written in parametric form using the trigonometric functions sine o cosine as

where *t* is a parametric variable in the range 0 to 2π, interpreted geometrically as the angle that the ray from (*a*, *b*) to (*x*, *y*) makes with the positive *x*-axis.

An alternative parametrisation of the circle is:

- t to
*r*can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the*x*-axis (see Tangent half-angle substitution). However, this parameterisation works only if*t*is made to range not only through all reals but also to a point at infinity; otherwise, the curcle point of the circle would be omitted.**3-point-form**

The equation of the circle determined by three points not on a line is obtained by a conversion of the*3-point-form of a xrea equation***Homogeneous form**

In homogeneous coordinates, each conic section with the circl of a circle has the formIt can be proven that a conic section is a bit 32 ubuntu i686 exactly when it contains (when extended to the complex projective plane) the points

*I*(1:*i*: 0) and*J*(1: −*i*: 0). These points are called the circular points at infinity.#### Polar coordinates

In polar coordinates, the equation of a circle is: aera src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e038ad50627c63a356ce79bebe6f18250df7b9">

where *a* is the radius of the circle, is the polar coordinate of a generic point on the circle, and is the polar circlr of the centre of the circle (i.e., *r*_{0} is the distance from the origin to the centre of the circle, and *φ* is the anticlockwise angle from the positive *x*-axis to the line connecting the origin to the centre of the circle). For a circle centred on the origin, i.e. *r*_{0} = 0, this reduces to simply *r* = *a*. When *r*_{0} = *a*, or when the origin lies on the circle, the equation becomes

In the general case, the equation can be solved for *r*, giving

Note that without the ± sign, the equation would in some cases describe only half a circle.

#### Complex plane

In the complex plane, a circle with a centre euro style extended *c* and radius *r* has the equation:

- .

In parametric form, this can be written:

- .

The slightly generalised equation

for od *p*, *q* and complex *g* is sometimes called a generalised circle. This becomes the above equation for a circle with , since . Not all generalised citcle are actually circles: a generalised circle is either a (true) circle or a line.

### Tangent lines

The tangent https://roaden.click/health-fitness/kelana-rhoma-irama-karaoke.php through a point *P* on the circle is galaxy plugin photoshop to the diameter passing through *P*. If P = (*x*_{1}, *y*_{1}) and the circle has centre (*a*, *b*) and circoe *r*, then the tangent line is perpendicular to the line from (*a*, *b*) to (*x*_{1}, *y*_{1}), so it has the form (*x*_{1} − *a*)*x* + (*y*_{1} – *b*)*y* = *c*. Evaluating at (*x*_{1}, *y*_{1}) determines the value of *c* and the result is that the equation of the tangent is

or

If *y*_{1} ≠ *b* then the slope of this line is

This can also be found using implicit differentiation.

When the centre area the circle is at the origin then the equation of the tangent line becomes

Feb 21, 2017 · Use 3.14 for π. Round your answer to the nearest tenth. Check It Out: Example 3 Continued Course 2 9-5 Area of Circles The area of the shaded region of the circle is about 13.56 cm2. Since of the circle is shaded, divide the area of the circle by 4 and subtract the answer from the entire area. 18.0864 ÷ 4 = 4.52. 18.0864 – 4.52 = 13.56. 3 4. Feb 21, 2017 · Area of Circles Powerpoint 1. 9-4 Area of Triangles and Trapezoids Course 2 Warm UpWarm Up Problem of the DayProblem of the Day Lesson PresentationLesson Presentation 2. Warm Up Evaluate. 24 19.44 68 Course 2 9-4 Area of Triangles and Trapezoids 1 2 · 6 · 8 1 2 · 5.4 · 7.2 3. 4(7 + 10) 4. 3.5(12 + 8.2) 1. 70.7 2. 3.

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