{"id":204,"date":"2022-04-13T08:42:34","date_gmt":"2022-04-13T08:42:34","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=204"},"modified":"2025-12-04T12:13:57","modified_gmt":"2025-12-04T12:13:57","slug":"l-6-arcs-and-chords","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-6-arcs-and-chords\/","title":{"rendered":"L.6 Arcs and chords"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Arcs and chords<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>Circle Basics<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>circle<\/strong> is a round shape with all points <strong>equidistant<\/strong> from the center.<\/li>\n\n\n\n<li>\ud83d\udc49 That equal distance is called the <strong>radius<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe2 <strong>What is a Chord?<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>chord<\/strong> is a <strong>line segment<\/strong> joining <strong>any two points<\/strong> on a circle.<\/li>\n\n\n\n<li>\ud83d\udc49 Every <strong>diameter<\/strong> is the <strong>longest chord<\/strong> in a circle.<\/li>\n\n\n\n<li>\ud83d\udc49 All diameters are chords, but <strong>not all chords are diameters<\/strong>.<\/li>\n\n\n\n<li>Example: Line AB inside a circle but not through center = chord.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe3 <strong>What is an Arc?<\/strong><\/h2>\n\n\n\n<p>An <strong>arc<\/strong> is a <strong>part (portion) of the circle\u2019s circumference<\/strong>.<\/p>\n\n\n\n<p>Two types:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Minor arc<\/strong>: smaller arc (less than 180\u00b0) \ud83c\udf19<\/li>\n\n\n\n<li><strong>Major arc<\/strong>: bigger arc (more than 180\u00b0) \ud83c\udf15<\/li>\n<\/ul>\n\n\n\n<p>The arc is usually named by <strong>two points<\/strong> on the circle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd36 <strong>Relationship Between Chords and Arcs<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equal chords subtend (form) <strong>equal arcs<\/strong>.<\/li>\n\n\n\n<li>Equal arcs subtend <strong>equal chords<\/strong>.<\/li>\n\n\n\n<li>\ud83d\udc49 <strong>Bigger chord = bigger arc<\/strong>, smaller chord = smaller arc.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd35 <strong>Perpendicular from Center to a Chord<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If you draw a <strong>perpendicular<\/strong> from the <strong>center<\/strong> of the circle to a chord,<br>\ud83d\udc49 it <strong>bisects<\/strong> the chord (cuts it into two equal parts). \u2702\ufe0f<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe9 <strong>Equal Distance Property<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Chords that are <strong>equidistant<\/strong> from the center are <strong>equal in length<\/strong>.<\/li>\n\n\n\n<li>The <strong>nearer<\/strong> a chord is to the center, the <strong>longer<\/strong> it becomes.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe0 <strong>Angle and Arc Relationship<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>central angle<\/strong> (angle at the center) formed by two radii equals the <strong>measure of the arc<\/strong> it intercepts.<br>\ud83d\udc49 Example: A central angle of <strong>60\u00b0<\/strong> makes an arc of <strong>60\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udfe3 <strong>Important Terms<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Radius (r)<\/strong>: center \u2192 any point on circle<\/li>\n\n\n\n<li><strong>Diameter (2r)<\/strong>: longest chord<\/li>\n\n\n\n<li><strong>Circumference<\/strong>: distance around the circle<\/li>\n\n\n\n<li><strong>Center<\/strong>: the middle point of the circle<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udf1f <strong>Real-Life Applications<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Arcs appear in <strong>bridges<\/strong>, <strong>wheels<\/strong>, <strong>windows<\/strong>, <strong>rainbows<\/strong>, and more. \ud83c\udf08\ud83d\udeb2<\/li>\n\n\n\n<li>Chords are used for <strong>construction<\/strong>, <strong>design<\/strong>, and <strong>geometry in engineering<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-26ea9651f2289e87824b30d20b12bd7c\" style=\"background-color:#d98f8f\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-ba9cebc5b50de8dc4c1990763c6c99d3\" style=\"color:#b00012\"><strong>What&nbsp;is the length of&nbsp; ST ?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-17.png\" alt=\"\" class=\"wp-image-11853\" style=\"width:288px;height:auto\"\/><\/figure><\/div>\n\n\n<p>ST = _______\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>RU&nbsp;and&nbsp;ST&nbsp;are arcs in a circle, and their corresponding chords are congruent. So,&nbsp;RU&nbsp;is congruent to&nbsp;ST.<\/p>\n\n\n\n<p>ST=RU=77\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#addceb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-a662d19232dfa8bd87788482f19a7038\" style=\"color:#b00012\"><strong>What&nbsp;is the measure of&nbsp;CD ?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-19.png\" alt=\"\" class=\"wp-image-11861\" style=\"width:300px;height:auto\"\/><\/figure><\/div>\n\n\n<p>CD = ________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>BE&nbsp;and&nbsp;CD&nbsp;are arcs in a circle, and their corresponding chords are congruent. So,&nbsp;BE&nbsp;is congruent to&nbsp;CD.<\/p>\n\n\n\n<p>CD = BE = 68\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9fdfbf\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-cfa21d2d3124e98451ddc86f0543d0fd\" style=\"color:#b00012\"><strong>What&nbsp;is the measure of&nbsp; HI ?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/Add-a-subheading-20.png\" alt=\"\" class=\"wp-image-11872\" style=\"width:304px;height:auto\"\/><\/figure><\/div>\n\n\n<p>HI = _______\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>FG&nbsp;and&nbsp;HI&nbsp;are arcs in a circle, and their corresponding chords are congruent. So,&nbsp;FG&nbsp;is congruent to&nbsp;HI.<\/p>\n\n\n\n<p>HI=FG=55\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88999\/748\/820\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image.png\" alt=\"\" class=\"wp-image-11941\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/88998\/305\/396\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-1.png\" alt=\"\" class=\"wp-image-11942\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Arcs and chords Key Notes : \ud83d\udd35 Circle Basics \ud83d\udfe2 What is a Chord? \ud83d\udfe3 What is an Arc? An arc is a part (portion) of the circle\u2019s circumference. Two types: The arc is usually named by two points on the circle. \ud83d\udd36 Relationship Between Chords and Arcs \ud83d\udd35 Perpendicular from Center to a Chord<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/l-6-arcs-and-chords\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.6 Arcs and chords&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-204","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=204"}],"version-history":[{"count":14,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204\/revisions"}],"predecessor-version":[{"id":18287,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204\/revisions\/18287"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}