Trigonometry For Dummies
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One way to describe the middle of a circle is to identify the centroid. This middle-point is the center of gravity, where you could balance the triangle and spin it around.

When you graph a circle, triangle, or line segment by using coordinate axes, then you can name these middle points with a pair of x- and y-coordinates. All you need to find these middles are the coordinates of some crucial other points on the respective figures.

If the endpoints of one diameter of a circle are (x1,y1) and (x2,y2), then the center of the circle has the coordinates

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You probably noticed that the center of a circle is the same as the diameter's midpoint. The center of the circle separates the diameter into two equal segments called radii (plural for radius).

The figure shows a circle with a diameter whose endpoints are (7,4) and (–1,–2). The center of the circle is at (3,1). The coordinates for the center were found by using the formula for the midpoint of a segment:

image1.jpg

You find the length of the diameter by using the distance formula:

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For the circle shown, the diameter is 10 units long.

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Next, you find the length of one of the radii. Either will do — they're the same length. In this example, figure the radius length from the center of the circle (3,1) to the endpoint of the diameter (7,4):

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The radius is 5 units long. But, of course, you expected this answer, because by definition, the radius is half the length of the diameter.

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Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.

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