Straight edge and compass geometry

[4thorns]

Hi all. The attached is in my case (and probably yours too!) a waste of time because I've already figured out how to do it using Autocad tools. I'd like to see if it can be done old school with no known numbers involved. Reminds me of trying to trisect an angle using a compass and a straight edge. (never did figure that one out)

In the attached drawing there are no known numbers other than the 90 degree angles on the right. The segments AB, BC and CD are random lengths. The arc (dashed line) runs through points A and C and is tangent to segment EF.

What I'm looking for is a way to draw the arc from point A to point D (Point G being the center of the arc) that is also tangent to line EF without using the dimensioning tools provided by autocad.

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[4thorns]

Try this instead.

http://i1287.photobucket.com/albums/a623/4thorns/Geometry_zps02b7801c.png

 

[rollupswx]

No dimensions used.
AutoCAD 2014.

 

[rollupswx]

This might be interesting.

 

[chicopee]

According to an article on this link mathworld.wolfram.com › Geometry › Trigonometry › Angles, only a few angle can be precisely trisected with a compass and straight edge, otherwise, you would get an approximation with these two tools.

 

[4thorns]

chicopee. After I read your reply I remembered that I did get it to work for a few angles. I want to say that they were 30, 60 and 90. Don't quite remember. Seems like high school was a hundred years ago! I do remember though going thru about a ream of paper trying to get it to work.

rollupswx. In your second pic you have the arc (circle). You didn't by any chance use a 3 point circle with tangent did you. I forgot to mention that tangent is cheating! If not then I would love to know how you came up with the diameter of the circle. Finding the plane of the center of the circle and center of the arc is the easy part (tho I did it a little different than you did). I drew a line perpendicular to the angled line (AD), through it's center. Finding the radius of the circle is what's stumping me!