{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T08:02:44+00:00","modifiedTime":"2016-03-26T08:02:44+00:00","timestamp":"2022-09-14T17:52:26+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":"Circle Basics for Geometry Problems","strippedTitle":"circle basics for geometry problems","slug":"circle-basics-for-geometry-problems","canonicalUrl":"","seo":{"metaDescription":"To solve geometry problems about circles, you will need to know the following circle theorems involving tangents, secants, and chords. These theorems can be use","noIndex":0,"noFollow":0},"content":"<p>To solve geometry problems about circles, you will need to know the following circle theorems involving tangents, secants, and chords. These theorems can be used to find information about angles, intercepted arcs, and length of segments of a circle. In addition, you find the standard and general form of a circle, the formulas for area and circumference, and the area of a sector of a circle.</p>\n<h2 id=\"tab1\" >Circle formulas</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">The circumference of a circle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470544.image0.png\" height=\"18\" alt=\"image0.png\" width=\"58\"/>\n </li>\n <li><p class=\"first-para\">The area of a circle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470545.image1.png\" height=\"18\" alt=\"image1.png\" width=\"22\"/>\n </li>\n <li><p class=\"first-para\">The area of a sector equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470546.image2.png\" height=\"29\" alt=\"image2.png\" width=\"440\"/>\n </li>\n <li><p class=\"first-para\"> </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470547.image3.png\" height=\"32\" alt=\"image3.png\" width=\"380\"/>\n </li>\n <li><p class=\"first-para\">Standard form of a circle:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470548.image4.png\" height=\"24\" alt=\"image4.png\" width=\"462\"/>\n </li>\n <li><p class=\"first-para\">General form of a circle:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470549.image5.png\" height=\"21\" alt=\"image5.png\" width=\"140\"/>\n </li>\n</ul>\n<h2 id=\"tab2\" >Circle theorems involving angles</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">The central angle equals the intercepted arc.</p>\n </li>\n <li><p class=\"first-para\">An inscribed angle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470550.image6.png\" height=\"29\" alt=\"image6.png\" width=\"144\"/>\n </li>\n <li><p class=\"first-para\">The interior vertical angles formed by two intersecting chords equal</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470551.image7.png\" height=\"36\" alt=\"image7.png\" width=\"81\"/>\n </li>\n <li><p class=\"first-para\">An exterior angle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470552.image8.png\" height=\"36\" alt=\"image8.png\" width=\"144\"/>\n </li>\n <li><p class=\"first-para\">A line tangent to a circle is perpendicular to the radius drawn to the point of tangency.</p>\n </li>\n</ul>\n<h2 id=\"tab3\" >Circle theorems involving lengths of segments</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">When a tangent and secant are drawn from the same exterior point,</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470553.image9.png\" height=\"22\" alt=\"image9.png\" width=\"434\"/>\n </li>\n <li><p class=\"first-para\">When two secants are drawn from the same exterior point,</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470554.image10.png\" height=\"34\" alt=\"image10.png\" width=\"420\"/>\n </li>\n</ul>","description":"<p>To solve geometry problems about circles, you will need to know the following circle theorems involving tangents, secants, and chords. These theorems can be used to find information about angles, intercepted arcs, and length of segments of a circle. In addition, you find the standard and general form of a circle, the formulas for area and circumference, and the area of a sector of a circle.</p>\n<h2 id=\"tab1\" >Circle formulas</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">The circumference of a circle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470544.image0.png\" height=\"18\" alt=\"image0.png\" width=\"58\"/>\n </li>\n <li><p class=\"first-para\">The area of a circle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470545.image1.png\" height=\"18\" alt=\"image1.png\" width=\"22\"/>\n </li>\n <li><p class=\"first-para\">The area of a sector equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470546.image2.png\" height=\"29\" alt=\"image2.png\" width=\"440\"/>\n </li>\n <li><p class=\"first-para\"> </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470547.image3.png\" height=\"32\" alt=\"image3.png\" width=\"380\"/>\n </li>\n <li><p class=\"first-para\">Standard form of a circle:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470548.image4.png\" height=\"24\" alt=\"image4.png\" width=\"462\"/>\n </li>\n <li><p class=\"first-para\">General form of a circle:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470549.image5.png\" height=\"21\" alt=\"image5.png\" width=\"140\"/>\n </li>\n</ul>\n<h2 id=\"tab2\" >Circle theorems involving angles</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">The central angle equals the intercepted arc.</p>\n </li>\n <li><p class=\"first-para\">An inscribed angle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470550.image6.png\" height=\"29\" alt=\"image6.png\" width=\"144\"/>\n </li>\n <li><p class=\"first-para\">The interior vertical angles formed by two intersecting chords equal</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470551.image7.png\" height=\"36\" alt=\"image7.png\" width=\"81\"/>\n </li>\n <li><p class=\"first-para\">An exterior angle equals</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470552.image8.png\" height=\"36\" alt=\"image8.png\" width=\"144\"/>\n </li>\n <li><p class=\"first-para\">A line tangent to a circle is perpendicular to the radius drawn to the point of tangency.</p>\n </li>\n</ul>\n<h2 id=\"tab3\" >Circle theorems involving lengths of segments</h2>\n<ul class=\"level-one\">\n <li><p class=\"first-para\">When a tangent and secant are drawn from the same exterior point,</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470553.image9.png\" height=\"22\" alt=\"image9.png\" width=\"434\"/>\n </li>\n <li><p class=\"first-para\">When two secants are drawn from the same exterior point,</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/470554.image10.png\" height=\"34\" alt=\"image10.png\" width=\"420\"/>\n </li>\n</ul>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8987"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":[{"articleId":175788,"title":"Trig Identities for Pre-Calculus","slug":"trig-identities-for-pre-calculus","categoryList":["academics-the-arts","math","pre-calculus"],"_links":{"self":"/articles/175788"}},{"articleId":147241,"title":"How to Use the Z-Table","slug":"how-to-use-the-z-table","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"/articles/147241"}},{"articleId":192609,"title":"How to Pray the Rosary: A Comprehensive 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Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8987"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","math","geometry"]},{"key":"isbn","values":["9781118853269"]}]\" id=\"du-slot-632214daa9247\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","math","geometry"]},{"key":"isbn","values":["9781118853269"]}]\" 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Circle Basics for Geometry Problems

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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To solve geometry problems about circles, you will need to know the following circle theorems involving tangents, secants, and chords. These theorems can be used to find information about angles, intercepted arcs, and length of segments of a circle. In addition, you find the standard and general form of a circle, the formulas for area and circumference, and the area of a sector of a circle.

Circle formulas

The circumference of a circle equals
The area of a circle equals
The area of a sector equals
Standard form of a circle:
General form of a circle:

Circle theorems involving angles

The central angle equals the intercepted arc.
An inscribed angle equals
The interior vertical angles formed by two intersecting chords equal
An exterior angle equals
A line tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Circle theorems involving lengths of segments

When a tangent and secant are drawn from the same exterior point,
When two secants are drawn from the same exterior point,

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

This article can be found in the category:

Geometry ,