In the common external tangent, the tangent does not cross between the two circles.
Two circles that do not intersect can either have a common external tangent or common internal Intersect at one point then they can either be externally tangent or internally tangent. Intersecting Circles: Two circles may intersect at two points or at one point. The following video gives the definitions of a circle, a radius, a chord, a diameter, secant, secant line, tangent, congruent circles, concentric circles, and intersecting circles.Ī secant line intersects the circle in two points.Ī tangent is a line that intersects the circle at one point.Ī point of tangency is where a tangent line touches or intersects the circle.Ĭongruent circles are circles that have the same radius but different centers.Ĭoncentric circles are two circles that have the same center, but a different radii. It touches the circle at point B and is perpendicular to the radius In the above diagram, the line containing the points B and C is a tangent to the circle. The point of tangency is where a tangent line touches the circle. TangentĪ tangent is a line that touches a circle at only one point.Ī tangent is perpendicular to the radius at the point ofĬontact. In the circle above, arc BC is equal to the ∠ BOC that is 45°. In the diagram above, the part of the circle from B to C forms an arc. The radii of a circle are all the same length. In the above diagram, O is the center of the circle andĪre radii of the circle. One advantage of this choice of radius was that he could very accurately approximate the chord of a small angle as the angle itself.The radius of the circle is a line segment from the center It was then a simple matter of scaling to determine the necessary chord for any circle. Ancient chord tables typically used a large value for the radius of the circle, and reported the chords for this circle. The half-angle identity greatly expedites the creation of chord tables. The chord function satisfies many identities analogous to well-known modern ones: Name Hipparchus is purported to have written a twelve volume work on chords, all now lost, so presumably a great deal was known about them. Much as modern trigonometry is built on the sine function, ancient trigonometry was built on the chord function. The last step uses the half-angle formula. In particular, an arc is any portion (other than the entire curve) of the circumference of a circle. In a graph, a graph arc is an ordered pair of adjacent vertices. The length of an arc is known as its arc length.
In general, an arc is any smooth curve joining two points. The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be (cos, sin ), and then using the Pythagorean theorem to calculate the chord length: There are a number of meanings for the word 'arc' in mathematics. The chord of an angle is the length of the chord between two points on a unit circle separated by that angle. The chord function is defined geometrically as in the picture to the left. Ptolemy of Alexandria compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1/2 degree to 180 degrees by increments of half a degree. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees. Chords were used extensively in the early development of trigonometry.
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