A geometry question

[khoshravan]

The circle C' with radius AB (r) and center B and angle alpha is given. I want to draw the triangle ABD in a way that CD=AB=r

Is there a way to draw it in AutoCAD ?
draw hexagon w compass and straightedge.dwg

For those who are interested, this is a way to trisect the angle alpha. Angle CBD is the trisect of alpha.

[eldon]

Here is one way to draw it in AutoCAD.

I had initial difficulty in identifying angle alpha, because it was not labelled in the drawing. However I have plumped for the angle so marked in my picture.

I drew an arc alpha and trisected it by using Divide. I drew a line to the third point, and mirrored it about a vertical line through B. This line I extended to C. Then I drew a line from A through C and extended it to D.

Check measurement reveals that C-D equals A-B equals r.

[khoshravan]

sorry I forgot to label the alpha but your guess is correct.

[eldon]

This morning, I see where I could have shortened the process a bit.

After drawing the line from B to the third point, then offset this line through A. Extend this line to the circle at A and the line to D.

[khoshravan]

This morning, I see where I could have shortened the process a bit.

After drawing the line from B to the third point, then offset this line through A. Extend this line to the circle at A and the line to D.

Actually this is more of a geometry question. You may remember from geometry that there are a set of questions which should be solved with only compass and straightedge (ruler with no mark).
Trisection of an angle is one of disputed questions which many believe that it is impossible to solve.

Off course for CAD users it is sort of nonsense. I was trying to solve that question.

If you are interested you can find more on http://en.wikipedia.org/wiki/Angle_trisection under item number 3.

[eldon]

Is there a way to draw it in AutoCAD ?

I know that the tri-section of an angle is a goal in geometry, and that was why, following your request to draw in AutoCAD, I was pleased to use facilities that are not available with manual means.