{"id":25446,"date":"2020-03-10T10:25:20","date_gmt":"2020-03-10T04:55:20","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=25446"},"modified":"2021-07-02T15:21:16","modified_gmt":"2021-07-02T09:51:16","slug":"kseeb-solutions-for-class-10-maths-chapter-4-additional-questions","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-10-maths-chapter-4-additional-questions\/","title":{"rendered":"KSEEB Solutions for Class 10 Maths Chapter 4 Circles Additional Questions"},"content":{"rendered":"

Students can Download Class 10 Maths Chapter 4 Circles Additional Questions Questions, Notes Pdf, KSEEB Solutions for Class 10 Maths<\/a> helps you to revise the complete Karnataka State Board Syllabus and score more marks in your in examinations<\/p>\n

Karnataka State Syllabus Class 10 Maths Chapter 4 Circles Additional Questions<\/h2>\n

I. Multiple Choice Questions:<\/span><\/p>\n

Question 1.
\nLine segment joining the centre and a point on the circle is called
\n(a) radius
\n(b) diameter
\n(c) Chord
\n(d) Arc
\nAnswer:
\n(a) radius<\/p>\n

Question 2.
\nPart of a circle is called
\n(a) Chord
\n(b) diameter
\n(c) Segment
\n(d) Arc
\nAnswer:
\n(d) Arc<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nThe biggest chord in a circle is called
\n(a) radius
\n(b) diameter
\n(c) chord
\n(d) Arc
\nAnswer:
\n(b) diameter<\/p>\n

Question 4.
\nThe region, bounded by a major arc and a chord is called
\n(a) Segment
\n(b) major segment
\n(c) minor segment
\n(d) major arc
\nAnswer:
\n(b) major segment<\/p>\n

Question 5.
\nThe length of the biggest chord is 8 cm then the value of radius is
\n(a) 8 cm
\n(b) 4 cm
\n(c) 3 cm
\n(d) 5 cm
\nAnswer:
\n(b) 4 cm<\/p>\n

Question 6.
\nHow many radius can be drawn in circle
\n(a) 1
\n(b) 2
\n(c) only 3
\n(d) many
\nAnswer:
\n(d) many<\/p>\n

Question 7.
\nAn angle in a semicircle is.
\n(a) 60\u00b0
\n(b) 30\u00b0
\n(c) 90\u00b0
\n(d) 180\u00b0
\nAnswer:
\n(c) 90\u00b0<\/p>\n

Question 8.
\nEqual chords of a circle are.
\n(a) Equidistant from the centre.
\n(b) Equal
\n(c) Unequal
\n(d) Not equidistant from the centre
\nAnswer:
\n(b) Equal<\/p>\n

Question 9.
\nIf the length of the chord increases its perpendicular distance from the centre.
\n(a) Increases
\n(b) Decreases
\n(c) Equal
\n(d) Constant
\nAnswer:
\n(b) Decreases<\/p>\n

Question 10.
\nThe perpendicular distance between the biggest chord and the centre is.
\n(a) zero
\n(b) Equal
\n(c) 9 cm
\n(d) 10cm
\nAnswer:
\n(a) zero<\/p>\n

Question 11.
\nIn a circle angles in the major segment are called.
\n(a) Obtuse angles
\n(b) Acute angles.
\n(c) Right angles
\n(d) Complete angle
\nAnswer:
\n(b) Acute angles.<\/p>\n

\"KSEEB<\/p>\n

Question 12.
\nIn a circle angles in the minor segment are called.
\n(a) Obtuse angles
\n(b) Acute angles.
\n(c) Right angles
\n(d) zero angle
\nAnswer:
\n(a) Obtuse angles<\/p>\n

Question 13.
\nIn a circle angles in the same segment are
\n(a) Not equal
\n(b) Right angles
\n(c) Equal
\n(d) zero angle.
\nAnswer:
\n(c) Equal<\/p>\n

Question 14.
\nCircles having the same centre but different radii are called.
\n(a) Congruent circles
\n(b) Concentric circles
\n(c) Equal circles
\n(d) None of these
\nAnswer:
\n(b) Concentric circles<\/p>\n

Question 15.
\nCircles having same radii but different centres are called
\n(a) Congruent circles
\n(b) Concentric circles
\n(c) Equal circles.
\n(d) Intersecting circles
\nAnswer:
\n(a) Congruent circles<\/p>\n

Question 16.
\nThe number of circles are drawn through three non-collinear points in a plane is.
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nAnswer:
\n(a) 1<\/p>\n

Question 17.
\nA line which intersects a circle in two points is called
\n(a) A secant
\n(b) A chord
\n(c) An arc
\n(d) A tangent
\nAnswer:
\n(a) A secant<\/p>\n

Question 18.
\nA line which intersects a circle in only one point is called
\n(a) A secant
\n(b) A tangent
\n(c) A chord
\n(d) A diameter
\nAnswer:
\n(b) A tangent<\/p>\n

Question 19.
\nA tangent to a circle intersects the circle is
\n(a) one point only
\n(b) Two points
\n(c) No point
\n(d) Three points
\nAnswer:
\n(a) one point only<\/p>\n

Question 20.
\nA secant of a circle intersects the circle in
\n(a) only one point
\n(b) Two points
\n(c) Three points
\n(d) No point
\nAnswer:
\n(b) Two points<\/p>\n

Question 21.
\nThe point where a tangent line intersects a circle is called the
\n(a) centre
\n(b) point of contact
\n(c) End-point
\n(d) None of these
\nAnswer:
\n(b) point of contact<\/p>\n

\"KSEEB<\/p>\n

Question 22.
\nThe angle between the tangent at any point of a circle and the radius through the point of contact is
\n(a) 60\u00b0
\n(b) 90\u00b0
\n(c) 45\u00b0
\n(d) 30\u00b0
\nAnswer:
\n(b) 90\u00b0<\/p>\n

Question 23.
\nHow many tangents can be drawn to a circle at any point of it?
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) None of these
\nAnswer:
\n(a) 1<\/p>\n

Question 24.
\nHow many parallel tangents can a circle have at the most?
\n(a) 1
\n(b) 2
\n(c) 4
\n(d) 3
\nAnswer:
\n(b) 2<\/p>\n

Question 25.
\nTwo circles of radii 5 cm and 3 cm touch each other externally. The distance between their centres is
\n(a) 5 cm
\n(b) 3 cm
\n(c) 2 cm
\n(d) 8 cm
\nAnswer:
\n(d) 8 cm<\/p>\n

Question 26.
\nTwo circles of radii 5 cm and 3 cm touch each other internally. The distance between their centres is
\n(a) 5 cm
\n(b) 3 cm
\n(c) 2 cm
\n(d) 8 cm
\nAnswer:
\n(c) 2 cm<\/p>\n

Question 27.
\nThe tangents at the endpoints of a diameter of circle are
\n(a) perpendicular
\n(b) parallel
\n(c) intersecting
\n(d) inclined at 60\u00b0
\nAnswer:
\n(b) parallel<\/p>\n

Question 28.
\nThe length of the tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is
\n(a) 3 cm
\n(b) 2 cm
\n(c) 5 cm
\n(d) 4 cm
\nAnswer:
\n(a) 3 cm<\/p>\n

Question 29.
\nTwo concentric circles of radii 5 cm, and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
\n(a) 8 cm
\n(b) 6 cm
\n(c) 4 cm
\n(d) 10 cm
\nAnswer:
\n(a) 8 cm<\/p>\n

Question 30.
\nHow many tangent lines can be drawn to a circle from a point outside the circle?
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4
\nAnswer:
\n(b) 2<\/p>\n

\"KSEEB<\/p>\n

Question 31.
\nHow many tangents can be drawn to a circle have
\n(a) 2
\n(b) infinitely many
\n(c) one
\n(d) no
\nAnswer:
\n(b) infinitely many<\/p>\n

Question 32.
\nIn the following figure, |PBA is
\n(a) 60\u00b0
\n(b) 30\u00b0
\n(d) 45\u00b0
\n(d) none of these
\n\"KSEEB
\nAnswer:
\n(a) 60\u00b0<\/p>\n

Question 33.
\nIn the following figure, Find AP if AB = 5 cm
\n(a) 5 cm
\n(b) 4 cm
\n(c) 3 ccm
\n(d) 2 cm
\n\"KSEEB
\nAnswer:
\n(a) 5 cm<\/p>\n

Question 34.
\nIn the following figure, find the perimeter of A APQ if AB = 6 cm.
\n(a) 10 cm
\n(b)12cm
\n(c) 15 cm
\n(d) 6 cm
\n\"KSEEB
\nAnswer:
\n(b)12cm<\/p>\n

Question 35.
\nIn the following Figure, find the length of the chord AB if PA = 4 cm and OP = 3 cm.
\n(a) 2 cm
\n(b) 4 cm
\n(c) 10cm
\n(d) 5 cm
\n\"KSEEB
\nAnswer:
\n(c) 10cm<\/p>\n

II. Short Answer Questions:<\/span><\/p>\n

Question 1.
\nDefine concentric circles.
\nAnswer:
\nCircles which are having same centre and different radii are called concentric circles.<\/p>\n

Question 2.
\nDefine congruent circles.
\nAnswer:
\nCircles which are having same radii & different centres are called congruent circles.<\/p>\n

Question 3.
\nDefine the sector of a circle.
\nAnswer:
\nThe region bounded by an arc of a circle and its two bounding radii is called sector.<\/p>\n

Question 4.
\nName the biggest chord of a circle.
\nAnswer:
\nDiameter<\/p>\n

Question 5.
\nWrite the formula to find the perimeter of a circle.
\nAnswer:
\nCircumference = C = 2nx.<\/p>\n

Question 6.
\nName the angle formed in a semi-circle is
\nAnswer:
\nRight angle<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nName the angle formed in a major segment.
\nAnswer:
\nAcute angle<\/p>\n

Question 8.
\nName the angle formed in a minor segment.
\nAnswer:
\nObtuse angle.<\/p>\n

Question 9.
\nThe length of the tangent to a circle from a point P, which is 25 cm away from the centre, is 24 cm. What is the radius of the circle?
\nAnswer:
\n\"KSEEB
\n\"KSEEB<\/p>\n

Question 10.
\nIn a quadrilateral, ABCD circumscribes a circle with centre O. If \u2220AOB = 110\u00b0, then find \u2220COD.
\nAnswer:
\n\"KSEEB<\/p>\n

Question 11.
\nWrite the relationship between radius and diameter.
\nAnswer:
\nd = 2r (or) r = d\/2<\/p>\n

Question 12.
\nAngles formed in a same segment are ________
\nAnswer:
\nEqual<\/p>\n

III. Long Answer Questions:<\/span><\/p>\n

Question 1.
\nIn the following figure if \u2220DAB = 60\u00b0
\nand \u2220ACB = 70\u00b0, find the measure of \u2220DBA.
\nAnswer:
\n\"KSEEB
\n\"KSEEB<\/p>\n

Question 2.
\nProve that the perpendicular from the centre of a circle to a chord, bisect the chord.
\nAnswer:
\n\"KSEEB
\nAB is the chord of a circle with centre O and OD \u22a5 AB. We have to prove that AD = DB
\nIn \u2206 ODA and \u2206 ODB.
\nOA = OB (radii)
\nOD = OD (common)
\n\u2220ODA = \u2220ODB = 90\u00b0 (OD \u22a5 AB)
\n\u2206 ODA = \u2206 ODB (R H S)
\nAD = DB [C.P.C.T].<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nIf two equal chords of a circle intersect within the circle, prove that the segments of an chord are equal to corresponding segment of the other chord.
\nAnswer:<\/p>\n

\"KSEEB
\nOL \u22a5 AB and OM \u22a5 CD are drawn and OP is joined.
\nIn \u2206 OLP and \u2206 OMP, since equal chords are at equal distance from centres.
\nOL = OM (OP common)
\n\u2220OLP = \u2220OMP =90\u00b0
\n\u2206 OPL \u2245 \u2206 OPM. (R H S)
\n=> PL = PM [C.P.C.T]
\nBut, AL = CM
\n=> AL – PL = CM – PM
\n=> AP = CP
\nAlso, AB – AP = CD – CP
\n\u2234BP = DP
\nThus, corresponding segments are equals.<\/p>\n

Question 4.
\nIf two interesting chords of a circle make equal angel with that: diameter passing through their point of intersecting. Prove that the chords are equal.
\nAnswer:
\n\"KSEEB
\nOM \u22a5 AB and ON\u22a5CD
\nIn \u2206 OME and \u2206 ONE
\n\"KSEEB
\nOE = OE (common)
\n\u2234 By A AS congruence
\n\u2206 OME \u2245 \u2206 ONE
\nOM = ON (C.P.C.T)
\n\u2234 AB = GD [Distance between the center to the chords equal.]
\n\u2234 Length of the chords are equal.<\/p>\n

Question 5.
\nTwo concentric circles of radii 13 cm and 5 cm are drawn. Find the length of the chord of the outer circle which touches the inner circle.
\nAnswer:
\n\"KSEEB
\nIn A OPB [P = 90\u00b0
\nOB2 = OP2 + BP2
\n(13)2 = (5)2 + BP2
\nBP2 = 165 – 25 = 144
\n\"KSEEB
\nAB = 2BP = 2 x 12 = 24cm<\/p>\n

Question 6.
\nTangents AP and AQ are drawn to circle with centre O, from an external point A. Prove that \u2220PAQ = 2\u2220OPQ
\nAnswer:
\n\"KSEEB
\n‘O’ is the center of a circle.
\nAP & AQ are tangents.
\nIn A POQ, OP = OQ [radius]
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nCircles C1<\/sub> and C2<\/sub> touch internally at a point A and AB is a chord at the circle C1<\/sub> intersecting C2<\/sub> at P. Prove that AP = PB.
\nAnswer:
\n\"KSEEB
\nJoin OA, OP and OB.
\n\"KSEEB
\nHYP OA = HYP OB [radii]
\nOP = OP [common]
\n\u2206 OAP \u2245 \u2206 OPB [by RHS theorem]
\nAP = PB [C.P.C.T]<\/p>\n

Question 8.
\nA circle is touching the side BC of \u2206 ABC at P. AB and AC when produced are touching the circle at Q and R respectively. Prove that AQ = V2<\/sub> (Perimeter of \u2206 ABC)
\nAnswer:
\n\"KSEEB
\nAQ = AR \u2192 (1) [tangents drawn from A]
\nBP = BQ \u2192 (2) [tangents drawn from B]
\nCQ = CR \u2192 (3) [tangents drawn from C]
\nPerimeter of \u2206 ABC = AB + BC + AC
\n= AB + BP + PC + AC
\n= AB + BQ + CR + AC
\n[From (1), (2) & (3)]
\n= AQ + AR
\n= AQ + AQ [\u2234 using(1)]
\nPerimeter of \u2206 ABC = 2 AQ
\nAQ = 1\/2 (Perimeter of \u2206 ABC)<\/p>\n

Question 9.
\nA straight line drawn through the point of contact of two circles with centres A and B intersect the circles at P and Q respectively. Show that AP and BQ are parallel.
\nAnswer:
\n\"KSEEB
\nIn \u2206 APC
\nAP = AC [radii of same circle]
\n\"KSEEB<\/p>\n

Question 10.
\nTwo circles with centres X and Y touch each other externally at P. Two diameters AB and CD are drawn one in each circle parallel to other. Prove that B, P and C are coliinear.
\nAnswer:
\n\"KSEEB
\n\u2234 APD and BPC are two intersecting lines
\n\u2234 BPC is a straight line
\n\u2234 B, P, C are coliinear.<\/p>\n

\"KSEEB<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Class 10 Maths Chapter 4 Circles Additional Questions Questions, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your in examinations Karnataka State Syllabus Class 10 Maths Chapter 4 Circles Additional Questions I. Multiple Choice Questions: Question 1. …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/25446"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=25446"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/25446\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=25446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=25446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=25446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}