Lines Tangent to an Arc - Can You Draw the Arc First?

[rmac]

I ran into an interesting SketchUp problem yesterday. Suppose you want to draw something like this in SketchUp:

I don't see an easy way to draw the arc in the specified position and then draw the two sides so that they are tangent to the arc. It would be easy to draw the two sides first and then draw the arc tangent to the sides, but that requires some high-dollar trigonometry to get the sides drawn correctly to start with.

Is there an easy way to do this?

-- Russ

[Lifesaver2000]

Ok, don't know if I got this right or not, but I just happened to be working in sketchup right before you posted, so thought I would give it a try.

What I did was draw a circle of the appropriate radius with the desired center point, then I drew lines to where they intersected with the circle. Then I used those intersection points as end points for an arc, drew the arc then deleted the circle.

Of course, I may have misunderstood the question. I'm not all that great with sketchup.

[Lifesaver2000]

Oh, I realize I didn't actually draw the arc first as you state, but since an arc is part of a circle, and I drew the circle first, I thought that might count.

[rmac]

Hmm. I tried it your way and a couple of times it looked like the line turned a magenta color when it looked like it was tangent to the circle. But I can't make it happen every time. I think you're on to something, though. I'll try to find something that explains the magenta line and report back.

Update, a few hours later:

I found out that the magenta line indicates inferences of one kind or another, such as when the line you are trying to draw is parallel or perpendicular to an axis or another line in the model. I'm pretty sure now that the inferences I was seeing earlier had nothing to do with whether or not the line was tangent to the circle.

So the question still stands ... is there an easy way to draw the picture in the original post without somehow precalculating the orientation of the two sides? I'm starting to think there isn't.

-- Russ

[Torch02]

I don't think you can without using a 1" radius circle as the "template" for your arc.

If you are willing to use the circle as a template, then these are the steps:

1) Choose your starting point

2) Move 4" right & 3" up from your starting point. This is the center of the concentric cirlces

3) Draw the two cirlces

4) Draw the 6" horizontal line

5) Draw the two side lines, starting from the bottom/horizontal line and ending them so they are tangent to the outer circle from Step 3

Note - it is a lot easier to judge whether the line is tangent to the circle if you make the line longer than necessary to reach the circle. If you draw the lines longer, it will be obvious if you have draw a chord (which intersects the arc twice) instead of a tangent.

[rmac]

Torch02,

I don't mind using the 1" radius circle, and I agree with everything except the last step. The problem is that Step 5 relies on the user's ability to judge when the lines are tangent to the circle, and it isn't going to be 100% accurate no matter how careful you are. My big question is whether SketchUp provides some way to have the tangent line snap into the exactly correct position, sort of like the way it makes it easy to snap to the exact endpoint or midpoint of an existing line, or the way it makes it easy to draw lines exactly parallel to the axes.

SketchUp does provide that snapping if you draw the lines first and the arc afterward, but that doesn't work easily in the example because (without some offline trig) you don't know anything about the sides of the figure except that they are tangent to the arc.

I think what we're discovering here is that SketchUp is not AutoCAD, and I guess that's to be expected.

-- Russ

[Torch02]

Roger, roger.

Although I still think that the human eye is pretty good at discerning between a chord and a tangent, especially as you zoom in on the intersection point.

I'll have to give it a try when I get home this afternoon.

[JMadson Custom Wood]

I think Russ' point is that close is not perfect.

I'm going to use the right line as a reference.

1. start with the 1" circle

2. Draw your horizontal bottom line.

3. Mark the bottom end of your tangent line.

4. Make a line 1" to the right of that mark that goes to the center of the circle.

5. Rotate this line by 90 degrees.

6. Make a finished line from your starting point in step 3 up to the intersection of the rotated line and the circle.

(disclaimer- I don't have access to sketchup right now and I don't think step 4 is right)

[Bob Lang]

The problem is that circles aren't really circles in SketchUp, the are multi-sided polygons. If you draw the circle and the baseline, then draw lines from the ends of the baseline, there will be an inference to the end points of one of the short lines that make up the apparent circle. If you zoom way in you can see this, and one of the points will appear to be tangent (at least more so than the other choices). You can increase the number of segments in the circle by typing the number after you start the circle command, but before you draw anything. (this is apparent through the measurements window)

That will get you close, the question is, "is that close enough?"

Bob Lang