# 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 = 60

^{0}. 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 = 45^{0}, ∠ A = 105^{0}. 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 60^{0}

**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 = 90^{0}. 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.