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NCERT Solutions for class 10 maths construction are thoroughly explained hare. These solutions are created by expert team at Careers360 keeping in mind of latest syllabus and pattern of CBSE 2023-24. These NCERT solutions provide a step-by-step approach to solving all questions and comprehensively discussed them in easy and simple language. These NCERT solutions for class 10 are created under NCERT guidelines, are designed to aid students in preparing for their board exams.
Get free access to construction class 10 solutions on Careers360 to improve your CBSE exam preparation. Each question of the NCERT exercises is solved using diagrams with a clear step-by-step procedure for the class 10 construction solution. These NCERT solutions can help students improve their understanding and clarify any doubts they may have. Also Students can download NCERT solutions for class 10 maths chapter 11 pdf using the link given below.
Also Read,
Determination of a Point Dividing a Line Segment Internally:
Given a line segment AB, a point P can be determined that divides AB internally in the ratio M : N using the formula: AP/AB = M/(M+N)
Construction of a Tangent to a Circle with Known Center - A tangent can be constructed at a specific point P on a circle with a known centre O. The tangent line is perpendicular to the radius OP.
Construction of a Tangent to a Circle without Known Center - Even without knowing the exact center of the circle, you can construct a tangent at a point P on the circle using geometric methods.
Construction of Tangents from an External Point to a Circle with Known Center - Tangents can be drawn from an external point E to a circle with a known centre O. The tangent lines are equal in length and angles between the radius and tangents are right angles.
Construction of Tangents from an External Point to a Circle without Known Center - Even without knowing the circle's center, you can construct tangents from an external point E to the circle using specific techniques.
Construction of a Similar Triangle with Given Scale Factor (m/n), m < n:
To construct a triangle similar to a given triangle ABC, but scaled down with a ratio m/n, the corresponding sides of the new triangle are m times smaller than the sides of ABC.
Construction of a Similar Triangle with Given Scale Factor (m/n), m > n:
Similarly, if the scale factor m/n is greater than 1, the corresponding sides of the new triangle are m times larger than the sides of ABC.
Free download NCERT Solutions for class 10 maths construction PDF for CBSE Exam.
NCERT Solutions for Maths Chapter 11 Construction Class 10th Excercise: 11.1
In each of the following, give the justification of the construction also:
Q1 Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Steps of construction:-
(i) Draw a line segment AB of measurement 7.6 cm (length).
(ii) Now draw an acute angle AC with line segment AB.
(iii) Now cut 13 equal points on the line AC where the zeroth point is A.
(iv) Join the 13th point with point B. So the new line is BA 13 .
(v) Now, from point A 5 draw a line parallel to BA 13 on line AB. Name the point as D.
The point D is the required point which divides the line segment in the ratio of 5: 8.
The length of the two parts obtained is 2.9 cm and 4.7 cm for AD and DB respectively.
Justification:- In the figure, we can see two similar triangles: and
Thus .
Steps of construction are:-
(i) Firstly draw a line segment AB of length 4 cm.
(ii) Now cut an arc of radius 5 cm from point A and an arc of 6 cm from point B.
(iii) Name the point of intersection of arcs to be point C.
(iv) Now join point AC and BC. Thus ABC is the required triangle.
(v) Draw a line AD which makes an acute angle with AB and is opposite of vertex C.
(vi) Cut three equal parts of line AD namely AA 1 , AA 2 , AA 3 .
(vii) Now join A 3 to B. Draw a line A 2 B' parallel to A 3 B.
(viii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
Steps of construction are:-
(i) Firstly draw a line segment AB of length 5 cm.
(ii) Now cut an arc of radius 6 cm from point A and an arc of 7 cm from point B.
(iii) Name the point of intersection of arcs to be point C.
(iv) Now join point AC and BC. Thus ABC is the required triangle.
(v) Draw a line AD which makes an acute angle with AB and is opposite of vertex C.
(vi) Cut seven equal parts of line AD namely AA 1 , AA 2 , AA 3 , AA 4 , AA 5 , AA 6 , AA 7 ,.
(vii) Now join A 5 to B. Draw a line A 7 B' parallel to A 5 B.
(viii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
Answer:
Steps of construction:-
(i) Draw a line segment AB of length 8 cm.
(ii) Cut arcs taking point A and point B as the center. Draw the line to intersect on line segment AB. Mark the intersecting point as point D.
(iii) Cut arc of length 4 cm on the same line which will be the altitude of the triangle.
(iv) Name the point as C. Then ABC is the isosceles triangle.
(v) Draw a line AX which makes an acute angle with AB and is opposite of vertex C.
(vi) Cut seven equal parts of line AX namely AA 1 , AA 2 , AA 3 .
(vii) Now join A 2 to B. Draw a line A 3 B' parallel to A 2 B.
(viii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
Steps of construction:-
(i) Draw a line segment BC with a measurement of 6 cm.
(ii) Now construct angle 60 o from point B and draw AB = 5 cm.
(iii) Join point C with point A. Thus ABC is the required triangle.
(iv) Draw a line BX which makes an acute angle with BC and is opposite of vertex A.
(v) Cut four equal parts of line BX namely BB 1 , BB 2 , BB 3 , BB 4.
(vi) Now join B 4 to C. Draw a line B 3 C' parallel to B 4 C.
(vii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
Steps of construction:-
(i) Draw a line segment BC.
(ii) Now draw an angle B = 45 o and
C = 30 o and draw rays in these directions.
(iii) Name the intersection of these lines as A.
(iv) Thus is the required triangle.
(v) Draw a line BX which makes an acute angle with BC and is opposite of vertex A.
(vi) Cut four equal parts of line BX namely BB 1 , BB 2 , BB 3 , BB 4.
(vii) Now join B 3 to C. Draw a line B 4 C' parallel to B 3 C.
(viii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
Steps of construction:-
(i) Draw a line segment AB having a length of 4 cm.
(ii) Now, construct a right angle at point A and make a line of 3 cm.
(iii) Name this point C. Thus ABC is the required triangle.
(iv) Draw a line AX which makes an acute angle with AB and is opposite of vertex C.
(v) Cut four equal parts of line AX namely AA 1 , AA 2 , AA 3 , AA 4 , AA 5 .
(vi) Now join A 3 to B. Draw a line A 5 B' parallel to A 3 B.
(vii) And then draw a line B'C' parallel to BC.
Hence AB'C' is the required triangle.
NCERT Solutions for Chapter 11 Class 10 construction Excercise: 11.2
Q1 In each of the following, give also the justification of the construction:
Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.
Steps of construction:-
(i) Taking point O as center draw a circle of radius 6 cm.
(ii) Now, name a point P which is 10 cm away from point O. Join OP.
(iii) Draw a perpendicular bisector of OP name the intersection point of bisector and OP as O'.
(iv) Now draw a circle considering O' as center and O'P as the radius.
(v) Name the intersection point of circles as Q and R.
(vi) Join PQ and PR. These are the required tangents.
(vii) Measure lengths of PQ = 8cm and PR = 8cm
Steps of constructions:-
(i) Taking point O as a center draw a circle of radius 4 cm.
(ii) Now taking O as center draw a concentric circle of radius 6 cm.
(iii) Taking any point P on the outer circle, join OP.
(iv) Draw a perpendicular bisector of OP.
(v) Name the intersection of bisector and OP as O'.
(vi) Now, draw a circle taking O' as center and O'P as the radius.
(vii) Name the intersection point of two circles as R and Q.
(viii) Join PR and PQ. These are the required tangents.
(ix) Measure the lengths of the tangents. PR = 4.47 cm and PQ = 4.47 cm.
Steps of construction:-
(i) Taking O as a center draw a circle of radius 3 cm.
(ii) Now draw a diameter PQ of this circle and extend it.
(iii) Mark two points R and S on the extended diameter such that OR = OS = 7 cm.
(iv) Draw the perpendicular bisector of both the lines and name their mid-points as T and U.
(v) Now, taking T and U as center draw circles of radius TR and QS.
(vi) Name the intersecting points of the circles with the first circles as V, W, X, Y.
(vii) Join the lines. These are the required tangents.
Steps of construction:-
(i) Draw a circle with center O and radius 5 cm.
(ii) Now mark a point A on the circumference of the circle. And draw a line AP perpendicular to the radius OA.
(iii) Mark a point B on the circumference of the circle such that AOB = 120 o . (As we know, the angle at the center is double that of the angle made by tangents).
(iv) Join B to point P.
(v) AP and BP are the required tangents.
Steps of construction:-
(i) Draw a line segment AB having a length of 8 cm.
(ii) Now, taking A as a center draw a circle of radius 4 cm. And taking B as a center draw a circle of radius 3 cm.
(iii) Bisect the line AB and name the mid-point as C.
(iv) Taking C as a center and AC as radius draw a circle.
(v) Name the intersection points of the circle as P, Q, R, S.
(vi) Join the lines and these are our required tangents.
Steps of construction:-
(i) Draw a line segment BC of length 8 cm.
(ii) Construct a right angle at point B. Now draw a line of length 6 cm. Name the other point as A.
(iii) Join AC. ABC is the required triangle.
(iv) Now construct a line BD on the line segment AC such that BD is perpendicular to AC.
(v) Now draw a circle taking E as a center (E is the midpoint of line BC) and BE as the radius.
(vi) Join AE. And draw a perpendicular bisector of this line.
(vii) Name the midpoint of AE as F.
(viii) Now, draw a circle with F as center and AF as the radius.
(ix) Name the intersection point of both the circles as G.
(x) Join AG. Thus AB and AG are the required tangents.
Steps of construction:-
(i) Draw a circle using a bangle.
(ii) Now draw 2 chords of this circle as QR and ST.
(iii) Take a point P outside the circle.
(iv) Draw perpendicular bisector of both the chords and let them meet at point O.
(v) Joinpoint PO.
(vi) Draw bisector of PO and name the midpoint as U.
(vii) Now, taking U as a center and UP as radius draw a circle.
(viii) Name the intersection point of both the circles as V and W.
(ix) Join PV and PW. These are the required tangents.
To divide a line segment in the given ratio.
To construct a pair of tangents from an external point to a circle.
To construct a triangle similar to a given triangle as per a given scale factor which may be greater than 1 or less than 1.
Also See
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | Constructions |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Learn some basic constructions like angles, triangles, and circles using compass and scale.
After this, go through some examples available in Cass 10 Maths Construction.
After covering the above processes, you can come to the practice exercises.
While practising the question, If you feel some trouble in any problem then take the help of NCERT solutions for Class 10 Maths Chapter 11 Constructions.
NCERT Solutions for Class 10 Maths Chapter 3 pdf download will be available soon. Till then you can download the webpage to practice the questions offline.
Keep working hard & happy learning!
NCERT Class 10 Maths chapter 11 constructions dividing a line segment in the given ratio, construct a pair of tangents from an external point to a circle, construct a triangle similar to a given triangle as per a given scale factor are the important topics in this chapter.
In order to perform well in the CBSE board exam, one must know the NCERT syllabus very well. NCERT solutions can help you, if stuck in NCERT problems while solving them. Also, NCERT solutions are provided by the experts who knows how to answer in the board exam in order to get good marks. For more problems refer to NCERT exemplar questions for Construction Class 10th chapter. For ease download NCERT solutions for class 10 maths chapter 11 pdf and study both online and offline mode.
Using the NCERT Solutions for chapter construction class 10 can give students a preview of the types of questions that may appear on their board exams, helping them to prepare effectively. These construction solutions class 10 are valuable resources that provide students with all the necessary information in a clear and concise format. The solutions cover all of the topics outlined in the NCERT syllabus set by the CBSE board.
The NCERT Solutions for Maths chapter 11 construction class 10th covers topics such as an introduction to constructions, the division of a line segment and construction of tangents to a circle, and a summary of all concepts presented in the chapter. By reviewing these solutions, students can clarify any doubts they have and practice additional questions.
To make it easier for students to learn, the solutions have been provided in PDF format, which students can download for free, and refer to them even without the internet. These NCERT Solutions for the construction of triangles class 10 can also be accessed online via the Careers360 website.
Exam Date:01 January,2025 - 14 February,2025
Exam Date:01 January,2025 - 14 February,2025
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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