Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3. Also, justify your construction.

Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are (2/3) of the corresponding sides of it.

Construct a triangle similar to a given such that each of its sides is of the corresponding sides of . It is given that AB = 5 cm, BC = 7 cm and .

Construct a triangle similar to a given such that each of its sides is of the corresponding sides of . It is given that BC = 6 cm, and .

Draw a in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to with its sides equal to of the corresponding sides of .

Construct a triangle with sides 5cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.

Draw a right triangle ABC in which AC = AB = 4.5 cm and . Draw a triangle similar to with its sides equal to th of the corresponding sides of .

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

Construct a in which AB = 5 cm. altitude CD = 3 cm. Construct a similar to such that side of is 1.5 times that of the corresponding sides of .

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

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

Construct a triangle similar to in which AB = 4.6 cm, BC = 5.1 cm, with scale factor 4 : 5.

Construct a triangle similar to a given with its sides equal to of the corresponding sides of . Write the steps of construction.

Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.

Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are 3/5 times the corresponding sides of the given triangle.

Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and . Then construct another triangle whose sides are 3/5 of the corresponding sides of .

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.

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.

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.

Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.

Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.

Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and . Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.