Class 10 Maths Constructions – Get here the Notes for Class 10 Maths Constructions. Candidates who are ambitious to qualify the Class 10 with good score can check this article for Notes. This is possible only when you have the best CBSE Class 10 Maths study material and a smart preparation plan. To assist you with that, we are here with notes. Hope these notes will help you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of Class 10 Maths for topic Constructions.

**Class:**10th**Subject:**Maths**Topic:**Constructions**Resource:**Notes

## CBSE Notes Class 10 Maths Constructions

Candidates who are pursuing in Class 10 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 10 Maths Constructions from this article.

**INTRODUCTION :** Construction is very important chapter of geometry. One of the aims of the studying construction is to acquire the skill of drawing figures

accurately.

In the previous classes you have learn how to construct angles of 300, 450, 60°, 90° and 120°. You have also learn how to construct some geometrical

figures like triangles, quadrilateral and circles, etc with the help of ruler and compass.

In this chapter, you will learn how to divide a line segment in a given ration (both internally and externally). You will also learn how to draw a triangle

similar to a given triangle with some given scale and to draw tangents from an interior point to a circle.

**DIVISION OF A LINE SEGMENT**

In order to divide a line segment internally in a given ratio m : n, where both m and n are positive integers, we follow the following steps :

**Given :** A line segment AB and a ratio min.

**Required :** To divide line segment AB in the ratio m: n.

**Steps of construction :**

(i) Draw a line segment AB of given length by using a ruler

(ii) Draw any ray AX making a suitable acute angle with AB.

(iii) Along AX draw (m + n) arcs intersecting the rays AX at A_{1}, A_{2},……,A_{m}, A_{m + 1},…..A_{m + n} such that AA_{1} = A_{1}A_{2} = = A_{m + n – 1} A_{m + n}

(iv) Join B A_{m + n}

(v) Through the point A_{m} draw a line parallel to A_{m + n} B by making’ ∠AA_{m}P = ∠AA_{m + n} B. Suppose this line meets AB at point P. The point P so obtained is the required point which divides AB internally in the ratio m: n.

**TO DRAW TANGENTS TO A CIRCLE FROM A POINT OUTSIDE IT, WHEN CENTRE OF THE CIRCLE IS KNOWN:**

**Given :** A circle with centre 0 and a point P outside it.

**Required :** To construct the tangents to the circle from point P.

**Steps of construction :**

(1) Join OP and bisect it. Let M be the mid-point of OP.

(ii) Taking M as centre and MO as radius, draw a circle to intersect the given circle in two points, say A and B.

(iii) Draw rays PA and PB.

Ray PA and PB are the required tangents from P to given circle.

**To draw tangents to a circle from a point outside it (when centre of the circle is not known)**

**Given :** A circle and a point P outside it.

**Required :** To draw tangents from point Pm the circle.

**Steps of construction :**

(i) Draw a secant PAB to intersect the circle at two points A and B.

(ii) Produce AP to a point C, such that PA = PC.

(iii) With BC as a diameter, draw a semi-circle.

(iv) Draw PD ⊥ CB, intersecting the semi-circle drawn in step (iii) at D.

(v) Taking PD as radius and P as centre, draw arcs to intersect the given circle at T and T’.

(vi) Draw rays PT and VT’. Rays PT and PT’ are the required tangents.

### Class 10 Key Points, Important Questions & Practice Papers

Hope these notes helped you in your schools exam preparation. Candidates can also check out the Key Points, Important Questions & Practice Papers for various Subjects for Class 10 in both Hindi and English language form the link below.

Class 10 Maths | कक्षा 10 गणित |

Class 10 Science | कक्षा 10 विज्ञान |

Class 10 Social Science | कक्षा 10 सामाजिक विज्ञान |

Class 10 English |

### Class 10 NCERT Solutions

Candidates who are studying in Class 10 can also check Class 10 NCERT Solutions from here. This will help the candidates to know the solutions for all subjects covered in Class 10th. Candidates can click on the subject wise link to get the same. Class 10 Chapter-wise, detailed solutions to the questions of the NCERT textbooks are provided with the objective of helping students compare their answers with the sample answers.

### Class 10 Mock Test / Practice

Mock test are the practice test or you can say the blue print of the main exam. Before appearing in the main examination, candidates must try mock test as it helps the students learn from their mistakes. With the help of Class 10 Mock Test / Practice, candidates can also get an idea about the pattern and marking scheme of that examination. For the sake of the candidates we are providing Class 10 Mock Test / Practice links below.

### Class 10 Exemplar Questions

Exemplar Questions Class 10 is a very important resource for students preparing for the Examination. Here we have provided Exemplar Problems Solutions along with NCERT Exemplar Problems Class 10. Question from very important topics is covered by Exemplar Questions for Class 10.

CBSE Class 10 Maths Notes Science Notes Social Science Notes English Notes