{"id":6079,"date":"2023-09-15T09:44:57","date_gmt":"2023-09-15T09:44:57","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6079"},"modified":"2023-09-15T09:45:56","modified_gmt":"2023-09-15T09:45:56","slug":"ncert-solutions-class-10-maths-chapter-10-circles-ex-10-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-10-circles-ex-10-1\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 10 Circles Ex 10.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 10 (Circles)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 10 Circles <\/strong>Exercise 10.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter : 10 Circles<\/strong> <\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-10-circles-ex-10-2\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 10.2<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 10.1<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1. How many tangents can a circle have?<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0<\/strong>A circle can have <strong>infinite<\/strong> tangents.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>2. Fill in the blanks.<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(i)<\/strong> A tangent to a circle intersects it in ________ point(s).<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(ii)<\/strong> A line intersecting a circle in two points is called a ________<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(iii)<\/strong> A circle can have ________ parallel tangents at the most.<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(iv)<\/strong> The common point of a tangent to a circle and the circle is called ________<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(i)<\/strong> A tangent to a circle intersects it in\u00a0<span style=\"text-decoration: underline;\"><strong>one<\/strong><\/span>\u00a0point(s).<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(ii)<\/strong> A line intersecting a circle in two points is called a\u00a0<strong><span style=\"text-decoration: underline;\">secant<\/span>.<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(iii)<\/strong> A circle can have\u00a0<strong><span style=\"text-decoration: underline;\">two<\/span>\u00a0<\/strong>parallel tangents at the most.<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(iv)<\/strong> The common point of a tangent to a circle and the circle is called the\u00a0<strong><span style=\"text-decoration: underline;\">point of contact<\/span>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at <\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>a point Q so that OQ = 12 cm. Length PQ is:<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">(A) 12 cm<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">(B) 13 cm<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">(C) 8.5 cm<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">(D) \u221a119 cm<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong>We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">And so, OP \u22a5 PQ<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">Using Pythagoras\u2019 theorem in triangle \u0394OPQ, we get,<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">OQ<sup>2<\/sup>\u00a0= OP<sup>2<\/sup>+PQ<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">(12)<sup>2\u00a0<\/sup>= 5<sup>2<\/sup>+PQ<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">PQ<sup>2<\/sup> = 144-25<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">PQ<sup>2<\/sup> = 119<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">PQ = \u221a119 cm<br \/>\n<\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">So,\u00a0<strong>option D,<\/strong>\u00a0i.e., \u221a119 cm, is the length of PQ.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4. Draw a circle and two lines parallel to a given line such that one is a tangent and the <\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>other, a secant to the circle.<br \/>\n<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0<\/strong><\/span><span style=\"color: #000000; font-family: Georgia, Palatino;\">In the above figure, XY and AB are two parallel lines. Line segment AB is the tangent at point C, while line segment XY is the secant.<\/span><\/p>\n<p><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff;\"><b><i>Go Back To Chapters<\/i><\/b><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 10 (Circles)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 10 Circles Exercise 10.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 10 Circles NCERT Class 10 Maths Solution Ex &#8211; 10.2 Exercise &#8211; 10.1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1099,1100,1044,1049,1048],"class_list":["post-6079","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-10-circles-solutions","tag-ncert-class-10-mathematics-exercise-10-1-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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