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To construct a diameter parallel to a given line, choose the chord to be perpendicular to the line. The circle having a given line segment as its diameter can be constructed by straightedge and compass, by finding the midpoint of the segment and then drawing the circle centered at the midpoint through one of the ends of the line segment.
Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter. By Thales' theorem, this is a right triangle with right angle at B. Let the length of A′B be c n, which we call the complement of s n; thus c n 2 +s n 2 = (2r) 2. Let C bisect the arc from A to B, and let C′ be the ...
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse.The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1]
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
The ratio of the circumference of any circle to its diameter is greater than but less than . This approximates what we now call the mathematical constant π . He found these bounds on the value of π by inscribing and circumscribing a circle with two similar 96-sided regular polygons .
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis ( major semiaxis ) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus , and ...
The angular diameter, angular size, apparent diameter, or apparent size is an angular separation (in units of angle) describing how large a sphere or circle appears from a given point of view. In the vision sciences , it is called the visual angle , and in optics , it is the angular aperture (of a lens ).