Draw a line segment of length 7 cm and divide it in the ratio2 : 3.

OR

Draw a circle of radius 4 cm and construct the pair of tangents to the circle from an external point, which is at a distance of 7 cm from its centre.

Construction Steps:

Step 1: Draw a line segment AB of length 7 cm.

Step 2: Draw a ray AX such that AB makes an acute angle.

Step 3: Locate points A₁, A₂, A₃, A₄ and A₅ such that

A₁ A₂ = A₂ A₃ = A₃ A₄ = A₄ A₅.

Step 4: Join A₅ and B.

Step 5: Through A₂, draw a line A₂P || A₅B intersecting AB at P.

The point P is the desired point which divides AB in the ratio

2: 3

OR

Steps of Construction:

1. Draw a line segment AB of length 8 cm.

2. Draw any ray AX, making an acute angle with AB.

3. Mark 5 (2 + 3) points A₁, A₂, .., A₅ on AX such that

AA₁ = A₁A₂ = .. = A₄A₅ by drawing equal arcs.

4. Join BA₅.

5. Since we want the ratio 2:3, through A₂, draw A₂C parallel to A₅B such that C lies on AB.

6. Thus AC : CB = 2 : 3.