{"id":26581,"date":"2022-01-13T17:55:03","date_gmt":"2022-01-13T12:25:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=26581"},"modified":"2022-02-08T16:40:30","modified_gmt":"2022-02-08T11:10:30","slug":"circles-class-9-notes-maths-chapter-11","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/circles-class-9\/notes-maths\/chapter-11\/","title":{"rendered":"Circles Class 9 Notes Maths Chapter 11"},"content":{"rendered":"<p>1. <strong>Circle:<\/strong> The collection of all points in a plane which are at a fixed distance from a fixed point in the plane is called a circle. The following examples of the circle are<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/40631807543_2472aeb790_o.png\" alt=\"Circles Class 9 Notes Maths Chapter 11 1\" width=\"532\" height=\"196\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>2. Basic Definition<\/p>\n<ul>\n<li><strong>Chord:<\/strong> Suppose, we take any two points on a circle, then the line segment PQ is called the chord of the circle.<br \/>\n<img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/40631807503_08a0e80cec_o.png\" alt=\"Circles Class 9 Notes Maths Chapter 11 2\" width=\"216\" height=\"194\" \/><\/li>\n<li><strong>Diameter:<\/strong> The chord which passes through the centre of the circle is called a diameter AB of the circle.<\/li>\n<li><strong>Arc:<\/strong> A piece of a circle between two points is called an arc. If P and Q are any two points on them, the PQ is an arc of the circle and it is denoted by AB.<\/li>\n<li><strong>Circumference:<\/strong> The length of the complete circle is called its circumference.<\/li>\n<li><strong>Semi-circle:<\/strong> A diameter of a circle divides it into two equal parts which an arc. Each of these two arcs is called a semi-circle.<\/li>\n<li><strong>Congruent Circles (Arc):<\/strong> Two circles are said to be congruent if and only if either of them can be superposed on the other so as to cover exactly.<\/li>\n<li><strong>Cyclic Quadrilateral:<\/strong> A quadrilateral ABCD is called cyclic if all the four vertices of it lie on a circle.<\/li>\n<li><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/32655597367_e024e206bd_o.png\" alt=\"Circles Class 9 Notes Maths Chapter 11 3\" width=\"172\" height=\"168\" \/><\/li>\n<li><strong>Common Chord:<\/strong> The intersection point of two circles is the common chord of the circle.<\/li>\n<\/ul>\n<p>3. Important Theorems<\/p>\n<ul>\n<li>The perpendicular from the centre of a circle to a chord bisects the chord and it is vice-versa.<\/li>\n<li>Equal chords of a circle (or of congruent circles) are equidistant from the centre.<\/li>\n<li>It two chords of a circle are equal, then their corresponding, arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.<\/li>\n<li>Congruent arcs of a circle subtend equal angles at the centre.<\/li>\n<li>The angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle.<\/li>\n<li>Angle in the same segment of a circle is equal.<\/li>\n<li>The sum of either pair of opposite angles of a cyclic quadrilateral is 180\u00b0 and vice-versa.<\/li>\n<li>The angle in a semi-circle is a right angle.<\/li>\n<li>If two chords of a circle are equal, then their corresponding arcs (minor, major or semi-circle) are congruent and vice-versa.<\/li>\n<\/ul>\n<div class=\"featured-snippet\"><\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Circle: The collection of all points in a plane which are at a fixed distance from a fixed point [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"Circles Class 9 Notes Maths Chapter 11","_yoast_wpseo_metadesc":"CBSE Class 9 Maths Notes Chapter 11 Circles \u00b7 The perpendicular from the centre of a circle to a chord bisects the chord and it is vice-versa.","custom_permalink":"study-materials\/circles-class-9\/notes-maths\/chapter-11\/"},"categories":[92,13,21],"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 Class 9 Notes Maths Chapter 11<\/title>\n<meta name=\"description\" content=\"CBSE Class 9 Maths Notes Chapter 11 Circles \u00b7 The perpendicular from the centre of a circle to a chord 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