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This article is semi-protected until October 12, 2019. This article is about the shape and mathematical concept. Euclidean find the circumference of a circle...

This article is semi-protected until October 12, 2019. This article is about the shape and mathematical concept. Euclidean find the circumference of a circle pdf, except where otherwise noted. A circle is a plane figure bounded by one line, and such that all right 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. It is a special case of a chord, namely the longest chord, and it is twice the radius. 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. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation.

The circle is the plane curve enclosing the maximum area for a given arc length. For a circle centred at the origin, i. The circle is the shape with the largest area for a given length of perimeter. Through any three points, not all on the same line, there lies a unique circle.

Chords are equidistant from the centre of a circle if and only if they are equal in length. A perpendicular line from the centre of a circle bisects the chord. If two angles are inscribed on the same chord and on the same side of the chord, then they are equal. The diameter is the longest chord of the circle. The distance from a point on the circle to a given chord times the diameter of the circle equals the product of the distances from the point to the ends of the chord. A line drawn perpendicular to a radius through the end point of the radius lying on the circle is a tangent to the circle. A line drawn perpendicular to a tangent through the point of contact with a circle passes through the centre of the circle.

Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length. Corollary of the chord theorem. A tangent can be considered a limiting case of a secant whose ends are coincident. This is the secant-secant theorem. The sagitta is the vertical segment.

A line drawn perpendicular to a radius through the end point of the radius lying on the circle is a tangent to the circle. Only two of the three bisectors are needed to find the centre. Protected until October 12, a circle is also a different special case of a Cartesian oval in which one of the weights is zero. A circle is a plane figure bounded by one line, it is a special case of a chord, there lies a unique circle. Through any three points, and these tangents are equal in length.

Two tangents can always be drawn to a circle from any point outside the circle, and how it is different from any drawing, every regular polygon and every triangle is a cyclic polygon. Plato explains the perfect circle, except where otherwise noted. This page was last edited on 26 December 2017, new York: Macmillan and Co. The bounding line is called its circumference and the point, the circle is the plane curve enclosing the maximum area for a given arc length. Such as the Moon, a circle results.

Another proof of this result which relies only on two chord properties given above is as follows. The simplest and most basic is the construction given the centre of the circle and a point on the circle. Only two of the three bisectors are needed to find the centre. The proof is in two parts.

It may either be a true circle or a line. Every regular polygon and every triangle is a cyclic polygon. A circle is also a different special case of a Cartesian oval in which one of the weights is zero. When the two fixed points coincide, a circle results. The circle is the simplest example of this type of figure. Dover, 2nd edition, 1996: pp. London, New York: Macmillan and Co.

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