One-time intersection of a line with a circle

[Sergey Kalev]

I need the line to touch the circle only at one point

Now, upon closer inspection, it can be seen that it does not touch the circle at just one point but creates intersections at two points

At the same time, I need the lower anchor point of the line to remain in place. Only the angle has changed, achieving a single point of contact with the circle

How can this be done, either by using a tool or a specific scheme?

[Myra Ferguson]

It sounds like Astute Graphics (provider or 3rd party plugins that do have a cost associated) Tangent Line Tool would help:

• SubScribe v2 - 03 Tangent Line Tools

[Jacob Bugge]

Sergey,

Illy (job description Adobe Illustrator) can do it for you at the full accuracy, within the general accuracy of Bezier circles, and she is always very friendly and helpful; I wonder whether external ways are more accurate.

You can use the following steps, Smart Guides being your friends, see the images below:

0) A circle and a crossing somewhat like those in your screenshot;

1) Select the circle so the centre shows, then ClickDrag with the Line Segment Tool from that to the intersection of the crossing (Smart Guides say center and intersection when you are within snapping distance), then Object>Path>Add Anchor Points to get its midpoint (shown in red;

2) Click somewhere on the Artboard with the Line Segment Tool and copy the Length, then Click somewhere on the Artboard with the Ellipse Tool and paste the copied Length for both Height and Width (also shown in red);

3) ClickDrag the circle from 3) by its centre to snap to the midpoint of the line from 2)

4) ClickDrag with the Line Segment Tool from the intersection of the circles to the intersection of the crossing (Smart Guides say intersection and intersection when you are within snapping distance); this is the lower part of the line you are seeking;

5) With the lower left Reference Point selected in the Transform panel, increase the Width or Height of the line if desired, remember to hold Ctrl/Cmd when pressing Enter, and maybe cut it off where desired afterwards.

Click to get closer, Click again to get closer still

[Kurt Gold]

You may also do a search for Hiroyuki Sato's script called "Common Tangents".

It may help.

[Jacob Bugge]

I tried that first, Kurt, but it failed me; initially with a 0 circle at the crossing giving no tangents (I believe it would have worked fine), then with small circle at the crossing and a corresponding offset (of the) circle because of the different bulging at the two sizes (larger for the larger) so when moving the lower end of the relevant tangent into the crossing it would cross the original circle.

Have you tried and succeeded?

[Kurt Gold]

Yes, Jacob. I drew a circle with a diameter of e.g. 100 mm. Then I drew a circle nearby with a diameter of 0,001 mm, selected both and ran Hiroyuki's script.

It worked fine (probably with a minor inaccuracy).

[Jacob Bugge]

Ah, of course, Kurt, the inignificant inacuracy being insignificant.

[rushbudgie]

https://youtu.be/Bo8Shotn4Sw

Try this guy, excellent info all things tangent.