Your calculator can find the sine of an angle instantly, and with a high degree of accuracy. The trigonometric sine function is the modern equivalent of the Greek chord function (which we will talk about shortly). What they didn't have was a simple formula for calculating the size of the central angle subtended by a chord of known length (or vice versa). They were certainly capable of constructing circles of a known diameter, and chords of a known length (you have probably done this at school with a pencil, a ruler and a pair of compasses). The Greeks knew that the size of the central angle subtended by a chord of a circle is proportional to the ratio of the length of the chord and the diameter of the circle. Chords of the same length subtend the same central angle.A chord's perpendicular bisector passes through the centre of the circle.Before we continue, there are a couple of things to keep in mind about chords of a circle: Until the third century BCE, however, the theorems developed by the Greeks were presented in geometric rather than algebraic terms. This of course included knowledge of the properties of chords, and angles inscribed in a circle. It is evident from what we know of the writings of classical Greek mathematicians, such as Archimedes and Euclid, that the Greeks already had an extensive knowledge of geometry. One of the greatest problems they faced was how to accurately measure angles. The branch of mathematics known as trigonometry began to emerge some three to four centuries BCE, as Greek astronomers and mathematicians searched for a consistent way of measuring and recording the movement and relative positions of various celestial bodies. In the common internal tangent, the tangent crosses between the two circles.Chord AB subtends arc AB and central angle α 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. The radius of the circle is a line segment from the center
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