I need to make two circles and have them to be tangent to each other. How can I do that?. My requirement is to do this at any point in those circles. Then what I need is that an additional line also tangent to those circles to go link those two circles.

This is better explained in this screenshot.

The first thing I need is that these two to be tangent at some random point. I figured that the only way to make this to happen for two circles is just turning on snap tool and snapping those at their smooth nodes by transforming the two circles into paths. But is this the only way? How can I achieve this for three circles and more? Because I don't know to make it to work for three circles.

Then there is my major problem, how can I make a line tangent to those?. I attempted to use guides but it isn't working right as when I place a line over it, it displays some shift to the right, not exactly tangent as I want. Maybe I am not using it correctly?.

The second thing I need to do is to put a radius which is perpendicular to that line and that radius has to have a small square. But how can I align those figures to fit nicely?. In the example I extended the radius outside the circle but it should had lie in the circle. I just can't find a way to do it right. Moreover how can I make that radius to depart from exactly the center of the circle?

Then the third thing I need is to put a nice dot in that intersection.

Then let's say I want to add some labels to write the lenghts, how do I insert a gap? and in addition to this put an object centered inside this gap? In this case the letters are paths as it is an svg I took from codecogs.

Here appears horizontally aligned,

But I wanted them to appear diagonally just in line with the radius. I just couldn't make it work right.

As it can be seen I tried using guides for this project but I can't make it to work properly. Would someone please be willing to teach me using some video?

Chemist116

How can I achieve this for three circles and more? Because I don't know to make it to work for three circles.

If you draw the 3 centerpoint of the circles you can use the extension render/draw from triangle ->contact triangle, that'll provide the radiuses of the circles. 

With some placer objects you can render circumcircles at the exact positions.

However that too is rather inaccurate due to inkscape's nature -using Béziers for aesthetics and not using circle arc element as geometry. 

Can use the polygon  tool for a more precise construction but if accuracy is what you are aiming at, maybe using a cad program would  be more fitting for the job.

Or another approach, like, using geogebra.

Inkscape is more fitting for illustrations, using it for geometric construction drawings takes some extra effort, considerations and some practice.

I just know of one SVG editor which uses collision detection for aligning perimeter of shapes. I´m not 100% sure Inkscape has something comparable.

Maybe the Apollonian Gasket extension can be of help:

Polygon

Maybe the Apollonian Gasket extension can be of help

There is such an extension? I need to check that out asap.

Yup - here: https://inkscape.org/~macbuse/★apollonian-master

and you might find these also interesting: https://inkscape.org/~jo.pol/★bobbin-lace-grids-and-patterns

@Chemist116 as for drawing/aligning tangents it's property per document and can be enabled there.

Create your 2 circles vertically overlapping and centered.  Use the - remove overlaps - tool in the align toolset.  This will establish their tangent.

Duplicate both and put it on a new layer.

Convert new circles to paths.  Delete the arc from right side node to top on upper circle and bottom circle.  Flip bottom circle vertically.  Join two right side nodes with new segment.

Keep the new segment but delete the remaining circle bits on this layer.

Duplicate new segment - change its color - rotate it in its bounding box until the line and edge are colinear.  Draw your radius line connected to this horizontal line.  If you need to, make a copy of the big circle - cut it in half - new line segment between polar nodes - delete rest of circle - find midpoint - cut new line segment - then move it to attach to horizontal segment.

Select new object - move so free end point overlaps endpoint of line spanning two circles.  Move anchor of new object to the common end point.  Rotate new object which is connected to radius line until the two lines are colinear.

Group everything together.  It is all on the upper layer in your stack.  Drop that layer down.  You now have your circle and line construct.  Rotate it until it is the angle you need or use transform tool for precise angles.

To do the text - create it on upper layer.  Create a white rectangle of proper size and put it below the text.

Your asset is done.

Remember to clean up duplicates.

Also, have you tried to align selected nodes at the bottom of the align toolset?

Remember to clean up duplicates.

Also, have you tried to align selected nodes at the bottom of the align toolset?

@Lazur I am using version 0.91 so I don't know if the extension you are saying is available in my version. I cannot use the latest version as it will not run properly in my laptop due limited resources as I am using a NB505 Toshiba.

It would be nice if you included some gif to show me how this is done. Can you do that?

For the rest of your comment I do know that I can use geogebra but I don't feel comfortable using it, and honestly I am not aiming at a fine precision. Just "nice looking" to a point where the stroke lines at least display nice adjustment and dont look wobbly or shaken from its intended position.

@Polygon I don't know what is Apollonian gasket or how would it be used here. Will you enlighten me?. By the way, it seems that it might require to install and since I am using a portable version of Inkscape probably I could not use it.

You mentioned that tangents can be done in document properties but I don't know how to do that. However I found this video https://www.youtube.com/watch?v=vQu-o8KHfgU
and it did helped me to trace a tangent to those as indicated.

But I don't know if that's what you meant with document properties. Can you show me please?.

There is still the fact of how would I join three circles without using additional extensions, can this be done?.

@NELCHAI It would be nice if you could show at least some screenshots of how to achieve that. Some steps I do understand but I am still novice on Inkscape. If you could make a gif that would be fantastic so I can see what's happening.

I wonder if is it really necesary to use many layers for this project?.
Regarding trying to align selected nodes, I don't know what are you referring to. 

But if you meant this one http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Align.html
Yes I used it before but I don't know if it would help here. Again it would be nice if you could include some gifs or screenshots as I am getting a bit lost from reading the steps you mentioned.

Maybe this:

For tangent circles, maybe this:

In Document Properties/Snap/Miscellaneous there is also an option "Snap Tangentially", that probably could help, at least in some of the above mentioned cases.

zerocinquanta

"Snap Tangentially", that probably could help, at least in some of the above mentioned cases.

Yes, instead of using the extension for the tangent line, snapping tangentially can be used. I usually will turn off the feature after using it, to avoid confusion later.