Geometry For Dummies
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An angle that intersects a circle can have its vertex inside, on, or outside the circle. This article covers angles that have their vertex inside a circle—so-called chord-chord angles. The measure of a chord-chord angle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

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For example, check out the above figure, which shows you chord-chord angle SVT. You find the measure of the angle like this:

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Look at the following figure:

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Here’s a problem to show how the formula plays out:

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To use the formula to find angle 1, you need the measures of arcs MJ and KL. You know the ratio of all four arcs is 1 : 3 : 4 : 2, so you can set their measures equal to 1x, 3x, 4x, and 2x. The four arcs make up an entire circle, so they must add up to 360°. Thus,

1x + 3x + 4x + 2x = 360

10x = 360

x = 36

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Now use the formula:

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That's a wrap.

About This Article

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About the book author:

Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses and standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. Ryan is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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