Procedure

1. Divide a straight line into a given number of equal parts.

1. Draw a line with the given length and mark it as AB.
2. Draw a line AC at any suitable angle.
3. Using a divider, cut off equal number of parts of the same length on the line AC.
4. Mark these points as 1’,2’,3’ and so on.
5. Join the last point with the point B on the given line.
6. Draw parallel lines from the rest of the points joining the line AB, dividing it into equal parts.

2. To inscribe a regular pentagon in a circle of a given diameter.

1. With AB as the given diameter, construct a circle.
2. Divide the diameter into 5 equal parts.
3. Draw arcs from A and B, with AB as the radius and mark the point of their intersection as C.
4. Join C with the second division on line AB and extend it to join the circle at D.
5. Join A-D which is the side of the pentagon.
6. From D mark an arc on the circumference of the circle with radius AD. Repeat the same to obtain points E, F and G
7. Join the points D-E, E-F and F-G. The figure A-D-E-F-G so obtained is a regular pentagon.

3. To construct a regular hexagon with a given side.

1. Draw the line with the given length and mark it as AB.
2. Extend this line to P such that BP=AB.
3. With B as the centre and AP as the diameter, draw a semicircle.
4. Divide this semicircle into 6 equal parts.
5. Draw a line from B joining the 2nd division. Mark the point as C.
6. Join B with the 3rd, 4th and 5th divisions and extend them.
7. Starting from the 2nd division, with radius AB, obtain an arc on B-3 and mark it as D.
8. With the same radius, Mark off E on the line B-4.
9. From E, mark F on the line B-5.
10. The figure so obtained by joining A-B-C-D-E-F is a regular hexagon.

4. To draw in a given equilateral triangle, three equal circles, each touching the other two sides and the other two circles.

1. Draw a side of an equilateral triangle with the given length. Name it AB.
2. With AB as the radius, draw arcs from A and B. Mark their point of intersection as C.
3. Join A-C and B-C.
4. Bisects angle A and B and extend the lines such that they pass the midpoint on the opposite sides of the triangle.
5. Drop a perpendicular from C, meeting these lines at their point of intersection O and extending it to the opposite side of the triangle. Mark it as P.
6. Bisect the angle CPB and mark point M where it meets the angle bisector of B.
7. Drop a perpendicular from M on the side of the triangle and name it as V.
8. With M as the centre and MV as the radius, draw a circle touching the two sides of the triangle.
9. Construct another circle with O as the centre and OM as the radius. Mark the points L and N where it cuts the other two lines.
10. Draw circles from L and N having a radius MV, such that they touch the two sides of the triangle and the other two circles