{"id":152177,"date":"2022-03-22T09:14:26","date_gmt":"2022-03-22T03:44:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/circles-3\/"},"modified":"2024-12-07T14:52:32","modified_gmt":"2024-12-07T09:22:32","slug":"circles-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/","title":{"rendered":"Circles"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Circle_Definition\" title=\"Circle Definition\">Circle Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Types_of_circle\" title=\"Types of circle\">Types of circle<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#How_to_Draw_a_Circle\" title=\"How to Draw a Circle?\">How to Draw a Circle?<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Also_Check\" title=\"Also Check\">Also Check<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Radius_of_Circle_r\" title=\"Radius of Circle (r)\">Radius of Circle (r)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Diameter_d_of_Circle\" title=\"Diameter (d) of Circle\">Diameter (d) of Circle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/#Properties_of_Circle\" title=\"Properties of Circle\">Properties of Circle<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>In mathematics, a circle is a specific type of ellipse with an eccentricity of zero, meaning its two foci coincide. It&#8217;s defined as the set of points equidistant from its center. The distance from the center to the circle&#8217;s edge is called the radius, while the diameter is twice the radius, dividing the circle in half.<\/p>\n<p>A circle is a fundamental 2D shape measured by its radius. It divides the plane into interior and exterior regions, resembling a curved line segment when bent to form a closed loop.<\/p>\n<p>This 2D figure has both area and perimeter. The perimeter, also known as the circumference, is the distance around the circle, while the area is the space enclosed by it in a 2D plane. These circle properties and formulas are important in mathematics and geometry.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Circle_Definition\"><\/span>Circle Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A circle is a closed two-dimensional shape where all points on the plane are equally distant from a central point called the &#8216;center.&#8217; Any line passing through the circle acts as a line of reflection symmetry, and the circle exhibits rotational symmetry for any angle. The formula for a circle in a plane is expressed as follows:<\/p>\n<p><strong>(x-h)<sup>2<\/sup> + (y-k)<sup>2<\/sup> = r<sup>2<\/sup><\/strong><\/p>\n<p>where,<\/p>\n<ul>\n<li>(x,y) are the coordinate points<\/li>\n<li>(h,k) is the coordinate of the centre of a circle<\/li>\n<li>r is the radius of a circle.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_circle\"><\/span>Types of circle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In Mathematics, there are several types of circles and related concepts:<\/p>\n<ol>\n<li><strong>Standard Circle:<\/strong> A standard circle is the most common type, with a fixed center and radius.<\/li>\n<li><strong>Concentric Circles:<\/strong> These are multiple circles that share the same center point but have different radii.<\/li>\n<li><strong>Tangent Circles:<\/strong> Tangent circles touch each other at exactly one point from the outside.<\/li>\n<li><strong>Secant Circle:<\/strong> A secant circle intersects another circle at two distinct points.<\/li>\n<li><strong>Inscribed Circle:<\/strong> An inscribed circle is the largest possible circle that can fit inside a polygon, touching all sides of the polygon.<\/li>\n<li><strong>Circumcircle:<\/strong> A circumcircle is the smallest circle that can enclose a polygon, touching all its vertices.<\/li>\n<li><strong>Unit Circle:<\/strong> A unit circle has a radius of 1 unit and is often used in trigonometry.<\/li>\n<li><strong>Degenerate Circle:<\/strong> This is a circle with a radius of 0, essentially a single point.<\/li>\n<li><strong>Hollow Circle:<\/strong> A hollow circle is just the boundary without any filled interior.<\/li>\n<li><strong>Ellipse:<\/strong> An ellipse is a stretched or compressed circle, where the distance between the two foci is greater than the length of the major axis.<\/li>\n<li><strong>Arc:<\/strong> An arc is a segment of a circle&#8217;s circumference.<\/li>\n<li><strong>Semicircle:<\/strong> A semicircle is half of a full circle, consisting of an arc and the diameter it is based on.<\/li>\n<li><strong>Quarter Circle:<\/strong> A quarter circle is one-fourth of a full circle, formed by cutting a circle into four equal parts.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"How_to_Draw_a_Circle\"><\/span>How to Draw a Circle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In this Class 10 math project focusing on circles, we provide a comprehensive explanation of circle construction, properties, and terminology. To grasp the concept of circles in a straightforward manner, explore the Class 10 circle project and engage in the following exercise:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-691695\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-54.jpg\" alt=\"How to Draw a Circle\" width=\"530\" height=\"350\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-54.jpg 530w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-54-300x198.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Begin with a blank sheet of paper and designate a central point, which we&#8217;ll call point O. Choose any random radius length, such as 3 cm. Using a ruler, measure 3 cm in various directions from point O, marking these points precisely 3 cm away from the central point. Feel free to mark as many points as desired, but maintain the 3 cm distance from point O in all directions.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Also_Check\"><\/span>Also Check<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li><strong>Regions of a Circle<\/strong><\/li>\n<li><strong>Circumference of a Circle<\/strong><\/li>\n<li><strong>Chords of a Circle<\/strong><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Radius_of_Circle_r\"><\/span>Radius of Circle (r)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A line segment that links the center of a circle to any point on its circumference is referred to as a &#8216;radius.&#8217; This distance is typically denoted by the symbol &#8216;R&#8217; or &#8216;r&#8217; in mathematical notation.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-691698\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-55.jpg\" alt=\"Radius of Circle\" width=\"490\" height=\"351\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-55.jpg 490w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-55-300x215.jpg 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Diameter_d_of_Circle\"><\/span>Diameter (d) of Circle<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A line segment with both endpoints on a circle is called a diameter. The diameter is always twice the length of the radius, expressed as d = 2r. Similarly, you can find the radius of the circle by using the formula r = d\/2, which derives from the diameter.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-691701\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-56.jpg\" alt=\"Diameter (d) of Circle\" width=\"520\" height=\"351\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-56.jpg 520w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/MicrosoftTeams-image-56-300x203.jpg 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Properties_of_Circle\"><\/span>Properties of Circle<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li>The circumference of a circle is uniformly distant from its center.<\/li>\n<li>A circle diameter divides it into two equal halves.<\/li>\n<li>Circles with identical radii are considered congruent.<\/li>\n<li>Circles that vary in size or have distinct radii are considered similar.<\/li>\n<li>The circle diameter serves as its longest chord and is precisely twice the length of the radius.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a circle is a specific type of ellipse with an eccentricity of zero, meaning its two foci coincide. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Circles","_yoast_wpseo_title":"Circles - Definition, Types of circle and Properties","_yoast_wpseo_metadesc":"A circle is a closed two-dimensional shape where all points on the plane are equally distant from a central point called the 'center.'","custom_permalink":"maths\/areas-related-to-circles\/circles-areas-related-to-circles\/"},"categories":[1],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Circles - Definition, Types of circle and Properties<\/title>\n<meta name=\"description\" content=\"A circle is a closed two-dimensional shape where all points on the plane are equally distant from a central point called the &#039;center.&#039;\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/areas-related-to-circles\/circles-areas-related-to-circles\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Circles - 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