Steps of Construction:

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

2. Locate 7 points A1, A2, A3, A4, A5, A6 and A7 on AX so that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6= A6A7

3. Join BA7.

4.Through the point A2, draw a line parallel to A7B at A2 intersecting AB at the point C . Then, AC : CB = 2 : 5.

Justification

Since A₂C is parallel to A₇B, therefore,

AA₅/A₅A₇ (By the Basic Proportionality Theorem) = AC/CB

AA By construction, AA₄/A₄A₇ Therefore, AC/CB = 2/5

This shows that C divides AB in the ratio 2 : 5.