Constructions

Exercise 1

In each of the following, give the justification of the construction also:

1.    Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

2.   Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are  of the corresponding sides of the first triangle.

3.   Construct a triangle with sides 6 cm, 6 cm and 7 cm and then another triangle whose sides are  of the corresponding sides of the first triangle.

4.   Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are  times the corresponding sides of the isosceles triangle.


5.   Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ ABC = 600. Then construct a triangle whose sides are  of the corresponding sides of triangle ABC.

6.   Draw a triangle ABC with side BC = 7 cm, ∠ B = 450, ∠ A = 1050. Then construct a triangle whose sides are  times the corresponding sides of Δ ABC.

7.    Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are  times the corresponding sides of the given triangle.

Exercise 2

8.   Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

9.   Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

10.  Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

11.   Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 600

12.   Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

13.   Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠ B = 900. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

14.   Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.