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# circle

 Definition/Summary Circle: the locus of all points on a Plane that are the same distance from a given point. Centre: that given point. Radius: any line (strictly, line segment) between the Centre and the Circle (also, the length of that line). Chord: any line segment between two points on the Circle. Diameter: any Chord though the Centre (also, the length of that Chord, which is twice the Radius). Focus and Eccentricity: a Circle is an Ellipse whose two Foci are both at the Centre, and whose Eccentricity is 0. Disc: a Circle together with its interior. Radian: the unit of angle, defined so that the angle round a whole Circle (360 degrees) is $2\pi$.

 Equations Diameter: $2 r$ Circumference: $2 \pi r$ Radian (a measure of angle): $\frac{360\deg}{2 \pi}$ Arc-length: $r \theta$ Chord-length: $2 r \sin\frac{\theta}{2}$ Curvature: $\frac{1}{r}$ Area: $\pi r^2$

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 Breakdown Mathematics > Geometry >> Plane Geometry