Triangle Question

First, I draw an oblique red line.

Next, I draw a blue line that is perpendicular to the red line

intersecting at point 1 and end at point 2.

How do I draw the magenta line (B line) that starts from point 3 and end at point 2, which is perpendicular to the green line (C line) that starts from point 4 and end at point 2.

Is the blue line exactly half the length of the red line (ie point #1 is the midpoint of the red line) or do you need to solve for any point along the red line?

Is the blue line exactly half the length of the red line (ie point #1 is the midpoint of the red line) or do you need to solve for any point along the red line?

 

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The blue line is not exactly half the length of the red line.

I need to solve for any point along the red line.

Brush up on pythgaros theorem it should be solvable and a/sina=b/sinb=c/sinc a triangle has 180 degrees, angle of red line is known, angle of blue line is known.

OK, so what are the known values? If the red line is the constant, you either need the distance from one end of the red line to point "1", or you need to know the length of the blue line. The animation below can be created by drawing any right triangle then a line perpendicular to the hypotenuse. then use Geometric Constraints > AutoConstrain. Add a dimensional constraint for the length of the red line plus one more for either distance 4-1 or distance

2-1 and it solves itself.

Draw a circle centered on the mid point of A and diameter A. The intersection of this circle and the blue line gives the third vertex of the triangle.

Updated animation based on eldon's suggestion

If I understand the problem correctly, you are given a line of fixed length (the red line) and then want to draw a line perpendicular to it at any place and then determine point 2 on the perpendicular line which will result in drawing lines B and C which are perpendicular to each other.

This is a great problem for using the parametric feature of AutoCAD! Try the following:

1. draw the red line (34).

2. From the Parametric tab menu apply a Fix constraint to both ends.

3. Draw a line approximately perpendicular to line 34.

4. Apply a perpendicular constraint between this line (12) and line 34.

5. Move the perpendicular line 12 to where you want it.

6. Apply a Fix constraint to one end of line 12.

7. Draw a line from point 3 to near where point 2 might be but not touching, line 12. Also draw a line from 4 close to 2.

At this point your drawing might look like this:

8. Now constraint the ends of the two new lines at points 3 and 4 with with Coincident constraints by clicking both lines first at junction 3 and then at junction 4. The Blue box indicate Coincident constraints.

9. Apply a Coincident constraint to the end of line coming from 3 by first clicking near the end by 2, then type o (for object) and click the perpendicular line (12). This should cause the end of the line from 3 to snap to the perpendicular line.

10. Apply a Coincident constraint to the end of the line from 4 to the end of line 32 near 2.

11. Apply an Angle constraint. Your drawing should look like this:

12. Edit the angle dimension to make it 90°.

13. Enjoy!

Yes, the circle method is more elegant.

If I understand the problem correctly, you are given a line of fixed length (the red line) and then want to draw a line perpendicular to it at any place and then determine point 2 on the perpendicular line which will result in drawing lines B and C which are perpendicular to each other.

 

This is a great problem for using the parametric feature of AutoCAD! Try the following:

1. draw the red line (34).

2. From the Parametric tab menu apply a Fix constraint to both ends.

3. Draw a line approximately perpendicular to line 34.

4. Apply a perpendicular constraint between this line (12) and line 34.

5. Move the perpendicular line 12 to where you want it.

6. Apply a Fix constraint to one end of line 12.

7. Draw a line from point 3 to near where point 2 might be but not touching, line 12. Also draw a line from 4 close to 2.

 

At this point your drawing might look like this:

 

 

8. Now constraint the ends of the two new lines at points 3 and 4 with with Coincident constraints by clicking both lines first at junction 3 and then at junction 4. The Blue box indicate Coincident constraints.

9. Apply a Coincident constraint to the end of line coming from 3 by first clicking near the end by 2, then type o (for object) and click the perpendicular line (12). This should cause the end of the line from 3 to snap to the perpendicular line.

10. Apply a Coincident constraint to the end of the line from 4 to the end of line 32 near 2.

11. Apply an Angle constraint. Your drawing should look like this:

 

12. Edit the angle dimension to make it 90°.

 

13. Enjoy!

 

Yes, the circle method is more elegant.

circle method is sublime