GEOMETRICAL CONSTRUCTIONS
GEOMETRICAL CONSTRUCTIONS
CONCEPT : TO DRAW TANGENT TO A CIRCLE
Board Weight age: 4 Marks
1.
Draw a “circle of 4 or 5 cm radius. Take a point P on it. At P draw a tangent to the
circle without using its center. Write steps of construction.
2.
To draw two tangents to a given circle from a point P lying outside the circle.
3.
Using ruler and compass, draw a tangent at a point P on a circle of radius 3 cm,
without using the center. Also write the steps of construction.
4.
Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 3.5 cm
from its center. Measure the lengths of these tangents. Use ruler and compass only
and write also the steps of construction.
5.
Use ruler and compass to draw two tangents to a circle of radius 2.5 cm from a point
6 cm away from its center. Write also the steps of construction.
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CONCEPT : TO DIVIDE A LINE INTERNALLY & EXTERNALLY
Divide a given straight line 5.5 cm long internally in the ratio 3:4.
Determine a point P on a line segment AB = 4.5 cm which divides it internally in the
ratio 2:3.
Divide a given straight line 5.5 cm long externally in the ratio 5:2.
Determine a point P which divides a line segment AB of length 3.5 cm externally in
the ratio 1:2.
Divide a line segment AB = 6.3 cm in the ratio 2:3:4.
Divide a line segment 6 cm long in the ratio 1:2:3:2.
Divide a given line segment PQ (i) internally (ii) externally in the ratio 3:5. Write the
steps of construction.
Divide a given straight line of length 4.5 cm (i) internally in the ratio 3:5; (ii)
externally in the ratio 4:5. Write the steps of construction.
CONCEPT : TO DRAW TRINAGLES WITH GIVEN MEDIAN AND
ALTITUDE
Construct a  ABC in which BC = 5 cm, A = 50° and altitude through A = 4 cm.
Construct a triangle ABC in which BC = 7.5 cm, A  60 and altitude through A is
3.7 cm. How many such triangle are possible? Write the steps of construction.
Graphics By : - Roshan Dhawan
- 38 -
Written By : - R. K. Badhan
GEOMETRICAL CONSTRUCTIONS
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Construct a  ABC in which base = 5 cm, A  55 and altitude through A is 3.4
cm.
Construct an  ABC in which BC = 6 cm, A  60 and the altitude through A is
4.5 cm. Measure the length of the median through A. Write the steps of
construction.
Construct a triangle ABC in which BC = 7 cm, A  70 and foot of the
perpendicular D on BC from A is 4.5 cm away from B.
Construct a  ABC in which BC = 6.5 cm, A  65 and the foot of the
perpendicular AD on BC is 4 cm away from B. Write also the steps of construction.
Construct a  ABC in which BC = 5 cm, A  70 and median AE through A is of
length 3.5 cm. Also, determine the length of the altitude drawn from A on the side
BC. Write the steps of construction also.
Construct a triangle ABC in which AB = 4.4 cm C  65 and median through C =
2.7 cm.
Construct a triangle ABC with AB = 4.4 cm, ACB  60 and the median through
C is of length 3.2 cm. Also, find the length of the altitude drawn from the vertex C
on AB.
Construct a triangle ABC in which AD = 4.4 cm, ACD  65 and the median
through C is of length 3.2 cm. Also, find the length of the altitude drawn from the
vertex C on AB.
Construct a triangle ABC in which BC = 6 cm, A  60 and median AD through A
is 5 cm long. Write the steps of construction. How many such triangle can be
constructed?
Construct a triangle ABC in which BC = 5 cm, A  70 and median AD through A
is of length 3.5 cm. Also, determine the length of the altitude drawn from A on the
side BC. Write the steps of construction also.
Construct a triangle ABC in which BC = 6 cm. A  50 and the median through A
is 5.5 cm. Find the length of the altitude drawn on BC from A. Write the steps of
construction.
Construction a triangle in which AB = 4.4 cm, C  60 and median through C = 3
cm. Write steps of construction.
Construct a triangle ABC in which BC = 6.5 cm, A  60 and median AD through
A is 3.5 cm long. Write steps of construction.
CONCEPT : TO DRAW CYCLIC QUADRILATERLAS
Construct a cyclic quadrilateral ABCD in which AC = 6 cm, BC = 4 cm, CD = 3.5
cm and B  90 .
Graphics By : - Roshan Dhawan
- 39 -
Written By : - R. K. Badhan
GEOMETRICAL CONSTRUCTIONS
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Construct a cyclic quadrilateral ABCD in which AB = 31 cm, BC = 6.4 cm, AC = 4.2
cm and AD = 2.4 cm.
Construct a cyclic quadrilateral ABCD in which AC = 6.5 cm, AB = 2 cm, AD = 2.5
cm, and B  60 .
Construct a cyclic quadrilateral ABCD in which AC = 6 cm, AB = 3 cm, AD = 4.5
cm and B  90 .
CONCEPT : TO DRAW SIMILAR TRIANGLES
Construct a triangle similar to a given triangle ABC such that each of its side is (2/3)
of the corresponding sides of the triangle ABC. It is given that AB = 4 cm, BC = 5
cm and AC = 6 cm. Also prove your assertion.
Construct a triangle similar to a given triangle XYZ with its sides equal to (3/4)th of
the corresponding sides of triangle XYZ. Write the steps of construction.
Construct a triangle similar to given triangle ABC such that each of its sides is
(5/7)th of the corresponding sides of triangle ABC. It is given that AB = 5 cm, BC =
7 cm and ABC  50 .
Draw a right triangle ABC in which AC = AB = 5.5 cm and A  90 . Draw a
triangle similar to triangle ABC which its sides equal to (5/4)th of the corresponding
sides of triangle ABC.
Construct a triangle ABC similar to a given isosceles triangle PQR with QR = 6 cm,
PR = PQ = 5 cm such that each of its sides is (6/7)th of the corresponding sides of the
triangle PQR. Write the steps of construction.
Construct a triangle ABC similar to a given isosceles triangle PQR with QR = 6 cm,
PR = PQ = 4 cm such that each of its side is (5/7)th of the corresponding sides of the
triangle PQR.
Construct a triangle ABC in which BC = 6.5 cm, mBAC  60 and median
through A is 4.5 cm. Construct a triangle A BC similar to triangle ABC with
BC  8 cm . Write the steps of construction.
Construction a triangle ABC in which AB = 5 cm, B  60 and altitude CD = 3 cm.
Construct a triangle AQR similar to triangle ABC such that each side of triangle
AQR is 1.5 times of the corresponding side of triangle ABC.
Construct a triangle ABC similar to a given equilateral triangle PQR with side 5 cm
such that each of its sides is (6/7)th of the corresponding sides of the triangle PQR.
Also draw the circumcircle of triangle ABC.
Graphics By : - Roshan Dhawan
- 40 -
Written By : - R. K. Badhan
GEOMETRICAL CONSTRUCTIONS
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CONCEPT : TO DRAW SIMILAR QUADRILATERALS
Draw a quadrilateral ABCD with AB = 3 cm, AD = 2.7 cm, DB = 3.6 cm, B  110
and BC = 4.2 cm. Construct a quadrilateral ABCD similar and similarly situated
to quadrilateral ABCD so that the diagonal DB may be 4.8 cm.
Draw a quadrilateral ABCD with AB = 4.5 cm, AD = 4 cm, BD = 5.4 cm, BC = 6.3
cm, B  110 . Construct another quadrilateral ABCD similar to quadrilateral
ABCD so that the diagonal DB = 7.2 cm.
Construct a quadrilateral similar to a given quadrilateral ABCD with its sides
(5/7)th of the corresponding sides of ABCD.
Construct a quadrilateral ABCD with AB = 4.5 cm, AD = 4 cm, DB = 4.4 cm,
B  130 and BC = 4 cm.
Draw any quadrilateral ABCD. Construct another quadrilateral AB C D similar
to the quadrilateral ABCD with each side equal to (4/5)th of the corresponding side
of quadrilateral ABCD. Write the steps of construction also.
Graphics By : - Roshan Dhawan
- 41 -
Written By : - R. K. Badhan