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| The Circle |
| The circle is a plane geometrical curve such that all its points lie at a fixed distance R, called the radius of the circle, from a point O, called the center of the circle. |
Up to now we have dealt with polygons. The sides of polygons are straight lines segments. The circle is a different kind of figures defined by a curve line.
The length of the curve, which is denoted by C, is called the circumference. The relationship between C and R is given by
where
which is read as “the number p (pi) is approximately equal to 3,14159” . Nevertheless, for many calculations the approximation
is used. One way to check this result is by drawing some circles, for each of them measure its radius R its circumference C and establish that the relationship C = 2p R with p = 3,14 is, in fact, right. One way of doing this is shown in detail in the following video (the audio is in Spanish)
The diameter D of the circle is defined by
The circumference C may now be written in terms of the diameter D
Let us now consider a straight line which intersects the circle in two points A and B. The segment of the line defined by A and B is called the AB chord.
Thus, the diameter is the longest of all possible chords in a given circle. One can also define the diameter by saying that is a chord which passes through the center O of the circle.
Suppose that the points A and B get closer together. Then, the length of the chord decreases. Consider the case in which they get so close together that the points A and B coalesce in just one point, which we call E. In this case the straight line is called the tangent to the circle at point E. The tangent at point E is perpendicular to the radius which joins point E and the center O of the circle.
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| · | Measure your World 2 |