Simple and Accurate TRISECTION Construction

This is an unorthodox yet accurate trisection construction that can be done with a
compass and unmarked straight edge.

It is also related to the theorem i stated earlier

Aim of the Construction: To trisect the given angle using an unmarked straight edge
and compass.

Given : Any angle BAC that is < or = 180˚

Outline Steps of Construction:

1)With the vertex of the given angle A as center and radius AB draw an arc BC that intersects the arms of the angle at B and C respectively.

2)Construct the bisector AD of the angle BAC .

3)Draw line A’D’ parallel to the line AD at a convenient distance AA’ from AD, that intersects arc BC at point D.

4)Construct the line DE perpendicular to AD , that intersects arc BC at point E.

5)Join lines BD and EC.

6)With D as center and radius DE mark off the point F on BD.

7)Construct a line perpendicular to line BC from point F, that intersects it at point G.

8)With A as center and radius AG draw the arc GO that intersects A’D’ at point H.Join GH.

9)Construct a line perpendicular to AD from point H ,that intersects AD at point I.

10)With H as center and radius equal to DE , mark off the point J on HG.

11)Construct the line JK perpendicular to line BC that intersects it at point K.

12)With A as center and radius AK draw an arc that intersects A’D’ at point L .Join KL.

13)Construct the line LN perpendicular to AD ,that intersects AD at point M .

14)With L as center and radius DE, mark off a point at distance =DE from point L.

15)If the point coincides with point K,then length of lines LK, LM and MO are equal and

AL and AN are the trisectors of the given angle BAC and the iterations can be stopped.Else continue iteration.