{"id":25773,"date":"2021-06-24T10:42:29","date_gmt":"2021-06-24T05:12:29","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=25773"},"modified":"2021-06-24T10:42:29","modified_gmt":"2021-06-24T05:12:29","slug":"ncert-solutions-for-class-9-maths-chapter-10-ex-10-4","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-10-ex-10-4\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4"},"content":{"rendered":"

These NCERT Solutions for Class 9 Maths<\/a> Chapter 10 Circles Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.4<\/h2>\n

Question 1.
\nTwo circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
\nSolution:
\nTwo circles with centre O, and A having radius 5 cm and 3 cm respectively.
\nThe distance between the centres i.e. OA = 4 cm CD is the common chord. OA is perpendicular to CD and bisects CD.
\n\"NCERT
\nOA \u22a5 CD and AC = AD
\nIn \u2206OAC, OC = 5 cm, OA = 4 cm.
\nBy Pythagoras theorem
\nAC2<\/sup> = OC2<\/sup> – OA2<\/sup>
\n\u21d2 AC2<\/sup> = 9
\n\u21d2 AC = 3 cm
\nHence CD passes through the centre of a smaller circle and equal to the diameter of the circle.
\nCD = 2AC = 2 \u00d7 3 = 6 cm<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nIf two equal chords of a circle intersect within the circle, prove that the segments of one chord are corresponding segments of the other chord.
\nSolution:
\nGiven: AB and CD are two equal chords of the circle which intersect each other at P.
\n\"NCERT
\nTo prove that: Segment ACB \u2245 Segment CBD.
\nProof: We have given,
\nchord AB = chord CD
\n\u2234 \\(\\widetilde{\\mathrm{AB}} \\cong \\widetilde{\\mathrm{CD}}\\)
\nWe know that, the segment made between congruent arcs and equal chords are congruent.
\n\u2234 Segment ACB \u2245 Segment CBD.<\/p>\n

Question 3.
\nIf two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
\nSolution:
\nGiven: AB and CD are two equal chords of a circle whose centre is O. Chord AB and CD intersect each other at E.
\n\"NCERT
\nTo prove that: \u22201 = \u22202
\nConstruction: Draw OM \u22a5 AB and ON \u22a5 CD, and join OE.
\nProof: In \u2206OME and \u2206ONE
\nOM = ON (Equal chords are equidistance from the centre)
\n\u2220OME = \u2220ONE (Each 90\u00b0)
\nOE = OE (Common)
\nSo, by R-H-S congruency condition
\n\u2206OME \u2245 \u2206ONE
\n\u22201 = \u22202 (By CPCT)<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nIf a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D. Prove that AB = CD (see Fig. 10.25)
\n\"NCERT
\nSolution:
\nLet OM be perpendicular from O on line l.
\nWe know that the perpendicular from the centre of a circle to a chord; bisect the chord. Since BC is a chord of the smaller circle and OM \u22a5 BC.
\n\u2234 BM = CM ……(i)
\nAgain, AD is a chord of the larger circle and OM \u22a5 AD.
\n\u2234 AM = DM ……(ii)
\nSubtracting equation (i) from (ii), we get
\nAM – BM = DM – CM
\nor, AB = CD.<\/p>\n

Question 5.
\nThree girls Reshma, Salma, and Mandeep are playing a game by standing on & circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Resma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?
\nSolution:
\nLet Reshma, Salma and Mandip are standing on the point R, S, and M respectively where O is the centre of the circle.
\n\"NCERT
\nRS = SM = 6m
\nOR = 5m
\n\u2206RSM is Issosclus Triangle
\n\u2234 SP \u22a5 RM and also P is mid-point of RM
\nRP = PM
\nar (\u2206ORS) = \\(\\frac {1}{2}\\) \u00d7 OS \u00d7 PR
\n= \\(\\frac {1}{2}\\) \u00d7 5 \u00d7 x …….(i)
\nDraw OT \u22a5 RS here OR = OS (Radii of circle)
\nSo, \u2206ORS is Issosceles Triangle
\n\u2234 RT = TS = 3 cm
\nIn right \u2206OTS,
\nOS = 5 cm, TS = 3 cm
\nUsing Pythagoras theorem,
\nOT2<\/sup> = OS2<\/sup> – TS2<\/sup>
\n\u21d2 OT2<\/sup> = (5)2<\/sup> – (3)2<\/sup>
\n\u21d2 OT2<\/sup> = 16
\n\u21d2 OT = \u221a16 = 4 cm
\nAgain, ar (\u2206ORS) = \\(\\frac {1}{2}\\) \u00d7 RS \u00d7 OT
\n= \\(\\frac {1}{2}\\) \u00d7 6 \u00d7 4 ……(ii)
\nFrom equation (i) and (ii)
\n\\(\\frac {1}{2}\\) \u00d7 5 \u00d7 x = \\(\\frac {1}{2}\\) \u00d7 6 \u00d7 4
\nor \\(\\frac {5x}{2}\\) = 12
\nx = \\(\\frac{12 \\times 2}{5}=\\frac{24}{5}\\)
\nWe have to calculate
\nRM = 2RP = 2 \u00d7 \\(\\frac{24}{5}\\) = \\(\\frac{48}{5}\\)
\n\u2234 RM = 9.6 m
\nDistance between Reshma and Mandip is equal to 9.6 m.<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nA circular park of a radius of 20 m is situated in a colony. Three boys Ankur, Syed, and David are sitting at an equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.
\nSolution:
\nLet three boys Ankur, Syed and David are sitting on the point A, B, and C respectively.
\nO is the centre of the circle.
\nAccording to question AB = BC = CA = x (Let)
\n\"NCERT
\nSo, \u2206ABC is an equilateral triangle
\nOA = OB = OC = Radius of die circle = 20 meter
\nJoin A, O and extand to D.
\nAs \u2206ABC is an equilateral triangle
\n\\(\\frac{\\mathrm{OA}}{\\mathrm{OD}}=\\frac{2}{1}\\)
\nor \\(\\frac{\\mathrm{20}}{\\mathrm{OD}}=\\frac{2}{1}\\) (\u2235 OA = 20 m)
\nOD = 10 meter
\nIn right angle triangle ACD
\n(AD)2<\/sup> = (CD)2<\/sup> + (AD)2<\/sup>
\n\u21d2 (x)2 = \\(\\left(\\frac{x}{2}\\right)^{2}\\) + (30)2<\/sup> (\u2235 AD \u22a5 BC and D is the mid point)
\n\u21d2 x2<\/sup> = \\(\\frac{x^{2}}{4}\\) + 900
\n\u21d2 x2<\/sup> – \\(\\frac{x^{2}}{4}\\) = 900
\n\u21d2 \\(\\frac{4 x^{2}-x^{2}}{4}\\) = 900
\n\u21d2 \\(\\frac{3 x^{2}}{4}\\) = 900
\n\u21d2 x2<\/sup> = \\(\\frac{900 \\times 4}{3}\\)
\n\u21d2 x2<\/sup> = 1200
\n\u21d2 x = \u221a1200
\n\u21d2 x = 20\u221a3 meteres
\nTherefore, the length of the string of each phone is 20\u221a3 meters.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.4 Question 1. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-9-maths-chapter-10-ex-10-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 9 Maths Chapter 10 Circles Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts. 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