{"id":31903,"date":"2018-10-10T10:15:31","date_gmt":"2018-10-10T10:15:31","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=31903"},"modified":"2020-11-25T15:53:14","modified_gmt":"2020-11-25T10:23:14","slug":"ml-aggarwal-class-10-solutions-for-icse-maths-chapter-17-chapter-test","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/ml-aggarwal-class-10-solutions-for-icse-maths-chapter-17-chapter-test\/","title":{"rendered":"ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test"},"content":{"rendered":"

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test<\/h2>\n

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths<\/a>. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test.<\/p>\n

ML Aggarwal Solutions<\/a>ICSE Solutions<\/a>Selina ICSE Solutions<\/a><\/p>\n

Question 1.<\/strong><\/span>
\nDraw a circle of radius 3 cm. Mark its centre as C and mark a point P such that CP = 7 cm. Using ruler and compasses only, Construct two tangents from P to the circle.<\/strong>
\nSolution:
\n<\/strong><\/span><\/p>\n

Steps of Construction :<\/p>\n

    \n
  1. Draw a circle with centre C and radius 3 cm.<\/li>\n
  2. Mark a point P such that CP = 7 cm.<\/li>\n
  3. With CP as diameter, draw a circle intersecting the given circle at T and S.<\/li>\n
  4. Join PT and PS.<\/li>\n
  5. Draw a tangent at Q to the circle given. Which intersects PT at D.<\/li>\n
  6. Draw the angle bisector of \u2220PDQ intersecting CP at E.<\/li>\n
  7. With centre E and radius EQ, draw a circle.
    \nIt will touch the tangent T and PS and the given circle at Q.
    \nThis is the required circle.<\/li>\n<\/ol>\n

    \"ML<\/p>\n

    Question 2.<\/strong><\/span>
    \nDraw a line AQ = 7 cm. Mark a point P on AQ such that AP = 4 cm. Using ruler and compasses only, construct :<\/strong>
    \n(i) a circle with AP as diameter.<\/strong>
    \n(ii) two tangents to the above circle from the point Q.<\/strong>
    \nSolution:
    \n<\/strong><\/span><\/p>\n

    Steps of construction :<\/p>\n

      \n
    1. Draw a line segment AQ = 7 cm.<\/li>\n
    2. From AQ,cut off AP = 4cm<\/li>\n
    3. With AP as diameter draw a circle with centre O.<\/li>\n
    4. Draw bisector of OQ which intersect OQ at M.<\/li>\n
    5. With centre M and draw a circle with radius MQ
      \nwhich intersects the first circle at T and S.<\/li>\n
    6. Join QT and QS.
      \nQT and QS are the tangents to the first circle.<\/li>\n<\/ol>\n

      \"ML<\/p>\n

      Question 3.<\/strong><\/span>
      \nUsing ruler and compasses only, construct a triangle ABC having given c = 6 cm, b = 1 cm and \u2220A = 30\u00b0. Measure side a. Draw carefully the circumcircle of the triangle.<\/strong>
      \nSolution:
      \n<\/strong><\/span><\/p>\n

      Steps of Construction :<\/p>\n

        \n
      1. Draw a line segment AC = 7 cm.<\/li>\n
      2. At C, draw a ray CX making an angle of 30\u00b0<\/li>\n
      3. With centre A and radius 6 cm draw an arc
        \nwhich intersects the ray CX at B.<\/li>\n
      4. Join BA.<\/li>\n
      5. Draw perpendicular bisectors of AB and AC intersecting each other at O.<\/li>\n
      6. With centre O and radius OA or OB or OC,
        \ndraw a circle which will pass through A, B and C.
        \nThis is the required circumcircle of \u2206ABC<\/li>\n<\/ol>\n

        \"ML<\/p>\n

        Question 4.<\/strong><\/span>
        \nUsing ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.<\/strong>
        \nSolution:
        \n<\/strong><\/span><\/p>\n

        Steps of Construction :<\/p>\n

          \n
        1. Draw a line XY and take a point D on it.<\/li>\n
        2. At D, draw perpendicular and cut off DA = 4 cm.<\/li>\n
        3. From A, draw rays making an angle of 30\u00b0
          \non each side of AD meeting the line XY at B and C.<\/li>\n
        4. Now draw perpendicular bisector of AC intersecting AD at O.<\/li>\n
        5. With centre O and radius OA or OB or OC
          \ndraw a circle which will pass through A, B and C.
          \nThis is the required circumcircle of \u2206ABC.<\/li>\n<\/ol>\n

          \"ML<\/p>\n

          Question 5.<\/strong><\/span>
          \nUsing ruler and compasses only :<\/strong>
          \n(i) Construct a triangle ABC with the following data: BC = 7 cm, AB = 5 cm and \u2220ABC = 45\u00b0.<\/strong>
          \n(ii) Draw the inscribed circle to \u2206ABC drawn in part (i).<\/strong>
          \nSolution:
          \n<\/strong><\/span>Steps of construction :<\/p>\n

            \n
          1. Draw a line segment BC = 7 cm.<\/li>\n
          2. At B, draw a ray BX making an angle of 45\u00b0 and cut off BA = 5 cm.<\/li>\n
          3. Join AC.<\/li>\n
          4. Draw the angle bisectors of \u2220B and \u2220C intersecting each other at I.<\/li>\n
          5. From I, draw a perpendicular ID on BC.<\/li>\n
          6. With centre, I and radius ID, draw a circle
            \nwhich touches the sides of \u2206ABC at D, E and F respectively.
            \nThis is the required inscribed circle.<\/li>\n<\/ol>\n

            \"ML<\/p>\n

            Question 6.<\/strong><\/span>
            \nDraw a triangle ABC, given that BC = 4cm, \u2220C = 75\u00b0 and that radius of circumcircle of \u2206ABC is 3 cm.<\/strong>
            \nSolution:
            \n<\/strong><\/span>Steps of Construction:<\/p>\n

              \n
            1. Draw a line segment BC = 4 cm<\/li>\n
            2. Draw the perpendicular bisector of BC.<\/li>\n
            3. From B draw an arc of 3 cm radius which intersects the perpendicular bisector at O.<\/li>\n
            4. Draw a ray CX making art angle of 75\u00b0<\/li>\n
            5. With centre O and radius 3 cm draw a circle which intersects the ray CX at A.<\/li>\n
            6. Join AB.
              \n\u2206ABC is the required triangle<\/li>\n<\/ol>\n

              \"ML<\/p>\n

              Question 7.<\/strong><\/span>
              \nDraw a regular hexagon of side 3.5 cm construct its circumcircle and measure its radius.<\/strong>
              \nSolution:
              \n<\/strong><\/span>Steps of construction:<\/p>\n

                \n
              1. Draw a regular hexagon ABCDEF whose each side is 3.5 cm.<\/li>\n
              2. Draw the perpendicular bisector of AB and BC
                \nwhich intersect each other at O.<\/li>\n
              3. Join OA and OB.<\/li>\n
              4. With centre O and radius OA or OB, draw a circle
                \nwhich passes through A, B, C, D, E and P.
                \nThen this is the required circumcircle.<\/li>\n<\/ol>\n

                \"ML<\/p>\n

                Question 8.<\/strong><\/span>
                \nConstruct a triangle ABC with the following data: AB = 5 cm, BC = 6 cm and \u2220ABC = 90\u00b0.<\/strong>
                \n(i) Find a point P which is equidistant from B and C and is 5 cm from A. How many such points are there ?<\/strong>
                \n(ii) Construct a circle touching the sides AB and BC, and whose centre is equidistant from B and C.<\/strong>
                \nSolution:
                \n<\/strong><\/span>Steps of Construction :<\/p>\n

                  \n
                1. Draw a line segment BC = 6 cm.<\/li>\n
                2. At B, draw a ray BX making an angle of 90\u00b0 and cut off BA = 5 cm.<\/li>\n
                3. Join AC.<\/li>\n
                4. Draw the perpendicular bisector of BC.<\/li>\n
                5. From A with 5 cm radius draw arc which intersects the perpendicular bisector of BC at P and P’.
                  \nThere are two points.<\/li>\n
                6. Draw the angle bisectors of \u2220B and \u2220C intersecting at 0.<\/li>\n
                7. From O, draw OD \u22a5 BC.<\/li>\n
                8. With centre O and radius OD, draw a circle which will touch the sides AB and BC.
                  \nThis is the required circle.<\/li>\n<\/ol>\n

                  \"ML<\/p>\n

                  Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test are helpful to complete your math homework.<\/p>\n

                  If you have any doubts, please comment below. APlusTopper<\/a>\u00a0try to provide online math tutoring for you.<\/p>\n","protected":false},"excerpt":{"rendered":"

                  ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test. ML Aggarwal SolutionsICSE SolutionsSelina ICSE Solutions Question 1. Draw a circle of […]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[6768],"tags":[6795,6794,6796,6775,6793,6799,6798,39620,6776,39619],"yoast_head":"\nML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test - A Plus Topper<\/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:\/\/www.aplustopper.com\/ml-aggarwal-class-10-solutions-for-icse-maths-chapter-17-chapter-test\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test\" \/>\n<meta property=\"og:description\" content=\"ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. 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Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Constructions Chapter Test. ML Aggarwal SolutionsICSE SolutionsSelina ICSE Solutions Question 1. 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