GEOMETRICAL CONSTRUCTIONS
GEOMETRICAL CONSTRUCTIONS
CONCEPT : TO DRAW TANGENT TO A CIRCLEBoard 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.
CONCEPT : TO DIVIDE A LINE INTERNALLY & EXTERNALLY6.Divide a given straight line 5.5 cm long internally in the ratio 3:4.
7.Determine a point P on a line segment AB = 4.5 cm which divides it internally in the ratio 2:3.
8.Divide a given straight line 5.5 cm long externally in the ratio 5:2.
9.Determine a point P which divides a line segment AB of length 3.5 cm externally in the ratio 1:2.
10.Divide a line segment AB = 6.3 cm in the ratio 2:3:4.
11.Divide a line segment 6 cm long in the ratio 1:2:3:2.
12.Divide a given line segment PQ (i) internally (ii) externally in the ratio 3:5. Write the steps of construction.
13.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 ALTITUDE14.Construct a in which BC = 5 cm, A = 50° and altitude through = 4 cm.
15.Construct a triangle ABC in which BC = 7.5 cm, and altitude through A is 3.7 cm. How many such triangle are possible? Write the steps of construction.
16.Construct a in which base = 5 cm, and altitude through A is 3.4 cm.
17.Construct an ABC in which BC = 6 cm, and the altitude through A is 4.5 cm. Measure the length of the median through A. Write the steps of construction.
18.Construct a triangle ABC in which BC = 7 cm, and foot of the perpendicular D on BC from A is 4.5 cm away from B.
19.Construct a ABC in which BC = 6.5 cm, and the foot of the perpendicular AD on BC is 4 cm away from B. Write also the steps of construction.
20.Construct a ABC in which BC = 5 cm, 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.
21.Construct a triangle ABC in which AB = 4.4 cm and median through C = 2.7 cm.
22.Construct a triangle ABC with AB = 4.4 cm, 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.
23.Construct a triangle ABC in which AD = 4.4 cm, 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.
24.Construct a triangle ABC in which BC = 6 cm, and median AD through A is 5 cm long. Write the steps of construction. How many such triangle can be constructed?
25.Construct a triangle ABC in which BC = 5 cm, 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.
26.Construct a triangle ABC in which BC = 6 cm. 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.
27.Construction a triangle in which AB = 4.4 cm, and median through C = 3 cm. Write steps of construction.
28.Construct a triangle ABC in which BC = 6.5 cm, and median AD through A is 3.5 cm long. Write steps of construction.
CONCEPT : TO DRAW CYCLIC QUADRILATERLAS29.Construct a cyclic quadrilateral ABCD in which AC = 6 cm, BC = 4 cm, CD = 3.5 cm and .
30.Construct a cyclic quadrilateral ABCD in which AB = 31 cm, BC = 6.4 cm, AC = 4.2 cm and AD = 2.4 cm.
31.Construct a cyclic quadrilateral ABCD in which AC = 6.5 cm, AB = 2 cm, AD = 2.5 cm, and .
32.Construct a cyclic quadrilateral ABCD in which AC = 6 cm, AB = 3 cm, AD = 4.5 cm and .
CONCEPT : TO DRAW SIMILAR TRIANGLES33.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.
34.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.
35.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 .
36.Draw a right triangle ABC in which AC = AB = 5.5 cm and . Draw a triangle similar to triangle ABC which its sides equal to (5/4)th of the corresponding sides of triangle ABC.
37.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.
38.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.
39.Construct a triangle ABC in which BC = 6.5 cm, and median through A is 4.5 cm. Construct a triangle similar to triangle ABC with . Write the steps of construction.
40.Construction a triangle ABC in which AB = 5 cm, 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.
41.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.
CONCEPT : TO DRAW SIMILAR QUADRILATERALS42.Draw a quadrilateral ABCD with AB = 3 cm, AD = 2.7 cm, DB = 3.6 cm, and BC = 4.2 cm. Construct a quadrilateral similar and similarly situated to quadrilateral ABCD so that the diagonal may be 4.8 cm.
43.Draw a quadrilateral ABCD with AB = 4.5 cm, AD = 4 cm, BD = 5.4 cm, BC = 6.3 cm, . Construct another quadrilateral similar to quadrilateral ABCD so that the diagonal = 7.2 cm.
44.Construct a quadrilateral similar to a given quadrilateral ABCD with its sides (5/7)th of the corresponding sides of ABCD.
45.Construct a quadrilateral ABCD with AB = 4.5 cm, AD = 4 cm, DB = 4.4 cm, and BC = 4 cm.
46.Draw any quadrilateral ABCD. Construct another quadrilateral 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 : - RoshanDhawan1Written By : - R.K.Badhan