{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T20:32:09+00:00","modifiedTime":"2016-03-26T20:32:09+00:00","timestamp":"2022-09-14T18:08:53+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"What You Need to Know About a Circle's Radius and Chords","strippedTitle":"what you need to know about a circle's radius and chords","slug":"what-you-need-to-know-about-a-circles-radius-and-chords","canonicalUrl":"","seo":{"metaDescription":"When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are rea","noIndex":0,"noFollow":0},"content":"<p>When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are really just three ideas; but two of the theorems work in both directions which brings the total to five):</p>\n<p><div class=\"imageBlock\" style=\"width:400px;\"><img src=\"https://www.dummies.com/wp-content/uploads/261983.image0.jpg\" width=\"400\" height=\"352\" alt=\"Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radiu\"/><div class=\"imageCaption\">Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radius of this circle.</div></div>\n</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><strong>Radii size: </strong>All radii of a circle are congruent.</p>\n</li>\n<li>\n<p class=\"first-para\"><strong>Perpendicularity and bisected chords: </strong></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">If a radius is perpendicular to a chord, then it bisects the chord.</p>\n</li>\n<li>\n<p class=\"first-para\">If a radius bisects a chord (that isn’t a diameter), then it’s perpendicular to the chord.</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><strong>Distance and chord size: </strong></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">If two chords of a circle are equidistant from the center of the circle, then they’re congruent.</p>\n</li>\n<li>\n<p class=\"first-para\">If two chords of a circle are congruent, then they’re equidistant from its center.</p>\n</li>\n</ul>\n</li>\n</ul>","description":"<p>When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are really just three ideas; but two of the theorems work in both directions which brings the total to five):</p>\n<p><div class=\"imageBlock\" style=\"width:400px;\"><img src=\"https://www.dummies.com/wp-content/uploads/261983.image0.jpg\" width=\"400\" height=\"352\" alt=\"Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radiu\"/><div class=\"imageCaption\">Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radius of this circle.</div></div>\n</p>\n<ul class=\"level-one\">\n<li>\n<p class=\"first-para\"><strong>Radii size: </strong>All radii of a circle are congruent.</p>\n</li>\n<li>\n<p class=\"first-para\"><strong>Perpendicularity and bisected chords: </strong></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">If a radius is perpendicular to a chord, then it bisects the chord.</p>\n</li>\n<li>\n<p class=\"first-para\">If a radius bisects a chord (that isn’t a diameter), then it’s perpendicular to the chord.</p>\n</li>\n</ul>\n</li>\n<li>\n<p class=\"first-para\"><strong>Distance and chord size: </strong></p>\n<ul class=\"level-two\">\n<li>\n<p class=\"first-para\">If two chords of a circle are equidistant from the center of the circle, then they’re congruent.</p>\n</li>\n<li>\n<p class=\"first-para\">If two chords of a circle are congruent, then they’re equidistant from its center.</p>\n</li>\n</ul>\n</li>\n</ul>","blurb":"","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> 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 as well as 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. 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Ryan is a member of the Authors Guild and the National Council of Teachers of Mathematics.<br /> <i>Geometry Workbook For Dummies</i> is Ryan’s fourth book. <i>Everyday Math for Everyday Life</i> was published in 2002, <i>Calculus For Dummies</i> (Wiley) in 2003, and <i>Calculus Workbook For Dummies</i> in 2005. 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What You Need to Know About a Circle's Radius and Chords

By: Mark Ryan and

Updated: 03-26-2016

Geometry For Dummies

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When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are really just three ideas; but two of the theorems work in both directions which brings the total to five):

Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radiu

Segment PG is a chord, segment AB is the diameter, and segment OC is the radius of this circle.

Radii size: All radii of a circle are congruent.
Perpendicularity and bisected chords:
- If a radius is perpendicular to a chord, then it bisects the chord.
- If a radius bisects a chord (that isn’t a diameter), then it’s perpendicular to the chord.
Distance and chord size:
- If two chords of a circle are equidistant from the center of the circle, then they’re congruent.
- If two chords of a circle are congruent, then they’re equidistant from its center.

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What You Need to Know About a Circle's Radius and Chords

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