Home UP BOARD Question Papers NCERT Solutions CBSE Papers CBSE Notes NCERT Books Motivational

Constructions Notes For Class 10 Chapter 11 Download PDF

Constructions Notes For Class 10 Chapter 11 Download PDF

Chapter 11 : Constructions Notes Download PDF

NCERT Notes For Mathematics Class 10

Chapter 11:- Constructions


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.


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 A1, A2,……,Am, Am + 1,…..Am + n such that AA1 = A1A2 = = Am + n – 1 Am + n

(iv) Join B Am + n
(v) Through the point Am draw a line parallel to Am + n B by making’ ∠AAmP = ∠AAm + 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.


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.

Constructions Notes for Class 10 

Please send your queries to ncerthelp@gmail.com you can aslo visit our facebook page to get quick help. Link of our facebook page is given in sidebar

Class and Subject List

Ncert Solution for class 6 to 12 download in pdf

CBSE Model test papars Download in pdf

NCERT Books Free Pdf Download for Class 5, 6, 7, 8, 9, 10 , 11, 12 Hindi and English Medium

Mathematics Biology Psychology
Chemistry English Economics
Sociology Hindi Business Studies
Geography Science Political Science
Statistics Physics Accountancy

CBSE Syllabus Class 6 to 9, 10, 11, 12 Maths, Science, Hindi, English ...

Last year CBSE Question paper for Class 6 to 9, 10, 11, 12 Maths, Science, Hindi, English ...

Important Links

Follow Us On

Face book page ncerthelp twitter page youtube page linkdin page



Please Share this webpage on facebook, whatsapp, linkdin and twitter.

Facebook Twitter whatsapp Linkdin

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.