## circle

circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone. The term circle is also used to refer to the region enclosed by the curve, more properly called a circular region. The radius of a circle is any line segment connecting the center and a point on the curve; the term is also used for the length r of this segment, i.e., the common distance of all points on the curve from the center. Similarly, the circumference of a circle is either the curve itself or its length of arc. A line segment whose two ends lie on the circumference is a chord; a chord through the center is the diameter. A secant is a line of indefinite length intersecting the circle at two points, the segment of it within the circle being a chord. A tangent to a circle is a straight line touching the circle at only one point, the point of contact, or tangency, and is always perpendicular to the radius drawn to this point. A circle is inscribed in a polygon if each side of the polygon is tangent to the circle; a circle is circumscribed about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference C of a circle is equal to π (see pi) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by Ar2. Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, i.e., constructing a square with an area equal to that of a given circle, using only a straight edge and compass; it was finally proved impossible in the late 19th cent. (see geometric problems of antiquity). In modern mathematics the circle is the basis for such theories as inversive geometry and certain non-Euclidean geometries. The circle figures significantly in many cultures. In religion and art it frequently symbolizes heaven, eternity, or the universe.

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## circle

cir·cle / ˈsərkəl/ (abbr.: cir. or circ.) • n. 1. a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). ∎  the line enclosing such a figure. ∎  something in the shape of such a figure: the lamp spread a circle of light. ∎  a group of people or things arranged to form such a figure: they all sat around in a circle. ∎  a movement or series of movements that follows the approximate circumference of such a figure: the astrological houses rotate in a circle. ∎  a dark circular mark below each eye, typically caused by illness or tiredness. ∎  a curved upper tier of seats in a theater.See also dress circle. 2. a group of people with a shared profession, interests, or acquaintances: she did not normally move in such exalted circles. • v. [tr.] move all the way around (someone or something), esp. more than once: the two dogs circle each other with hackles raised | [intr.] we circled around the island. ∎  [tr.] (from the air) move in a ring-shaped path above (someone or something), esp. more than once: they were circling the airport. ∎  [intr.] (circle back) move in a wide loop back toward one's starting point. ∎  (often be circled) form a ring around. ∎  draw a line around: circle the correct answers. PHRASES: come (or turn) full circle return to a past position or situation, esp. in a way considered to be inevitable. go around (or around and around) in circles inf. do something for a long time without achieving anything but purposeless repetition. run around in circles inf. be fussily busy with little result.

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# Circle

A circle can be defined as a closed curved line on which every point is equally distant from a fixed point within it. Following is some of the terminology used in referring to a circle:

1. The fixed point is called the center of the circle (C in Figure 1).

2. A line segment joining the center to any point on the circle is the radius of the circle (CA in Figure 1).

3. A line segment passing through the center of the circle and joining any two points on the circle is the diameter of the circle (DB in Figure 1). The diameter of a circle is twice its radius.

4. The distance around the circle is called the circumference of the circle.

5. Any portion of the curved line that makes up the circle is an arc of the circle (for example, AB or DA in Figure 1).

6. A straight line inside the circle joining the two end points of an arc is a chord of the circle (DE in Figure 1).

## Mathematical relationships

One of the interesting facts about circles is that the ratio between their circumference and their diameter is always the same, no matter what size the circle is. That ratio is given the name pi (π ) and has the value of 3.141592+. Pi is an irrational number. That is, it cannot be expressed as the ratio of two whole numbers. The + added at the end of the value above means that the value of pi is indeterminate: you can continue to divide the circumference of any circle by its diameter forever and never get an answer without a remainder.

The area of any circle is equal to its radius squared multiplied by π, or: A = π r2. The circumference of a circle can be found by multiplying its diameter by π (C = π D) or twice its radius by π (C = 2πr).

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# Circle

a set or series of parts connected to form a whole; a company assembled about a central point or topic of interest; a circular ring of persons or things. See also company, ring.

Examples: circle of action, 1752; of admirers, 1793; of acquaintances, 1752; of doctrine, 1531; of fallacy, 1646; of foliages, 1713; of glory, 1595; literary circle; circle of onlookers, 1875; of pleasures, 1759; of passion, 1768; of possibilities, 1644; of probability, 1851; of sciences, 1854; of stars, 1611.

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## circle

circle circle the wagons unite in defence of a common interest (originally North American, with reference to the defensive position of a wagon train under attack).
the wheel has come full circle the situation has returned to what it was in the past, as if completing a cycle, with reference to Shakespeare's King Lear, by association with the wheel fabled to be turned by Fortune and representing mutability.

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## circle

circle sb. XIV. ME. cercle — (O)F. :- L. circulus, dim. of circus ring (see CIRCUS); later respelt after L. OE. circul was an adoption directly from the Latin, but did not survive.
So circle vb. XIV. — L. circulāre, or from the sb.

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## circle

circle Plane geometric figure that is the locus of points equidistant from a fixed point (the centre). This distance is the radius (r). The area of a circle is πr2 and its perimeter (circumference) is 2πr.

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## circle

circlecackle, crackle, grackle, hackle, jackal, mackle, shackle, tackle •ankle, rankle •Gaskell, mascle, paschal •tabernacle • ramshackle •débâcle, diarchal, matriarchal, monarchal, patriarchal, sparkle •rascal •deckle, freckle, heckle, Jekyll, shekel, speckle •faecal (US fecal), treacle •chicle, fickle, mickle, nickel, pickle, prickle, sickle, strickle, tickle, trickle •besprinkle, crinkle, sprinkle, tinkle, twinkle, winkle, wrinkle •fiscal •laical, Pharisaical •vehicle • stoical • cubicle • radical •medical, paramedical •Druidical, juridical, veridical •syndical •methodical, periodical, rhapsodical, synodical •Talmudical • graphical • pontifical •magical, tragical •strategical •alogical, illogical, logical •dramaturgical, liturgical, metallurgical, surgical •anarchical, hierarchical, monarchical, oligarchical •psychical •angelical, evangelical, helical •umbilical • biblical • encyclical •diabolical, follicle, hyperbolical, symbolical •dynamical, hydrodynamical •academical, agrochemical, alchemical, biochemical, chemical, petrochemical, photochemical, polemical •inimical • rhythmical • seismical •agronomical, anatomical, astronomical, comical, economical, gastronomical, physiognomical •botanical, Brahmanical, mechanical, puritanical, sanicle, tyrannical •ecumenical •geotechnical, pyrotechnical, technical •clinical, cynical, dominical, finical, Jacobinical, pinnacle, rabbinical •canonical, chronicle, conical, ironical •tunicle • pumpernickel • vernicle •apical • epical •atypical, prototypical, stereotypical, typical •misanthropical, semi-tropical, subtropical, topical, tropical •theatrical •chimerical, clerical, hemispherical, hysterical, numerical, spherical •calendrical •asymmetrical, diametrical, geometrical, metrical, symmetrical, trimetrical •electrical • ventricle •empirical, lyrical, miracle, panegyrical, satirical •cylindrical •ahistorical, allegorical, categorical, historical, metaphorical, oratorical, phantasmagorical, rhetorical •auricle • rubrical • curricle •classical, fascicle, neoclassical •farcical • vesicle •indexical, lexical •commonsensical, nonsensical •bicycle, icicle, tricycle •paradoxical • Popsicle • versicle •anagrammatical, apostatical, emblematical, enigmatical, fanatical, grammatical, mathematical, piratical, prelatical, problematical, sabbatical •impractical, practical, syntactical, tactical •canticle •ecclesiastical, fantastical •article, particle •alphabetical, arithmetical, heretical, hypothetical, metathetical, metical, parenthetical, poetical, prophetical, reticle, synthetical, theoretical •dialectical •conventicle, identical •sceptical (US skeptical) • testicle •analytical, apolitical, critical, cryptanalytical, diacritical, eremitical, geopolitical, hypercritical, hypocritical, political, socio-political, subcritical •deistical, egoistical, logistical, mystical, papistical •optical, synoptical •aeronautical, nautical, vortical •cuticle, pharmaceutical, therapeutical •vertical • ethical • mythical • clavicle •periwinkle • lackadaisical •metaphysical, physical, quizzical •whimsical • musical •Carmichael, cervical, cycle, Michael •unicycle • monocycle • motorcycle •cockle, grockle •corncockle • snorkel •bifocal, focal, local, univocal, varifocal, vocal, yokel •archducal, coucal, ducal, pentateuchal •buckle, chuckle, knuckle, muckle, ruckle, suckle, truckle •peduncle, uncle •parbuckle • carbuncle • turnbuckle •pinochle • furuncle • honeysuckle •demoniacal, maniacal, megalomaniacal, paradisiacal, zodiacal •manacle • barnacle • cenacle •binnacle • monocle • epochal •reciprocal •coracle, oracle •spectacle •pentacle, tentacle •receptacle • obstacle • equivocal •circle, encircle •semicircle