topic Re: How to draw a circle tangent to two lines, trough two specific points? in AutoCAD Forum

How to draw a circle tangent to two lines, trough two specific points?

Anonymous — Mon, 23 Nov 2020 04:20:30 GMT

Hi!

I've had this problem for a while and can't seem to figure it out myself, so here goes:

I have two lines and need a circle tangent to both, but only to one point of each line. If I've got it correctly there should only be one solution to the problem no matter the lines or their angles or so on.

Thanks in advance!

Re: How to draw a circle tangent to two lines, trough two specific points?

imadHabash — Mon, 23 Nov 2020 05:16:42 GMT

Hi,

I suggest to try Geometric constraints which control the relationships of objects with respect to each other .

Re: How to draw a circle tangent to two lines, trough two specific points?

parkr4st — Mon, 23 Nov 2020 11:27:49 GMT

post the lines and diameter of the circle

parallel lines have infinite solutions but one diameter circle

crossing lines have multiple solutions i.e. if lines make an X four solutions for any diameter circle many solutions with varying diameters

lines make a V one solution per diameter = infinite solutions

non-parallel non-intersecting lines one solution per diameter infinite diameters = equal many solutions.

Re: How to draw a circle tangent to two lines, trough two specific points?

Anonymous — Mon, 23 Nov 2020 13:36:10 GMT

Here are the lines in question:

Lines.dwg is both lines with the tangent points marked.
Lines2.dwg is somewhat the intended result, but with intersections.

I don't have the radius of the circle or any other variable.

Re: How to draw a circle tangent to two lines, trough two specific points?

Kent1Cooper — Mon, 23 Nov 2020 13:53:06 GMT

[Written before seeing Message 4's drawings] There will be a solution only if the two specific points are the same distance from the intersection of the Lines [or virtual intersection, if they don't meet each other]. There's a [white] Circle tangent to both [red] Lines at both [green] Points in the left arrangement that fits that description. But that's not possible in the other two, in which the [dashed white] Circle is tangent to the lower Line at the lower Point, and passes through the other Point, but clearly cannot be tangent to the other Line.

There would be an Ellipse that would be tangent to both Lines at both Points in the middle and right images. Finding it would be a challenge in the middle image, but easy in the right one where the Lines are perpendicular.

EDIT: An eye-balled approximation in your drawing:

Re: How to draw a circle tangent to two lines, trough two specific points?

Anonymous — Mon, 23 Nov 2020 14:13:02 GMT

How would I go about finding that elipse?

Re: How to draw a circle tangent to two lines, trough two specific points?

Kent1Cooper — Mon, 23 Nov 2020 16:25:29 GMT

@Anonymous wrote:

How would I go about finding that elipse?

That's a real challenge, if even possible definitively, when the Lines are not perpendicular. In fact, there are an infinite number of solutions. My approximation is tangent to one Line at one of the Ellipse's quadrant points, which limits the solutions, but maybe that should not be assumed. And even given that assumption, that tangency condition could be at the Point on the other Line instead, with a different Ellipse. Even where a Circle solution is possible, there are an infinite number of possible Ellipse solutions at different aspect ratios, with an axis along the angle bisector:

I think at the very least you would need to come up with some more specific criteria, such as that it needs to be tangent at a quadrant point, and if so, at which of the two Points, or something.

Re: How to draw a circle tangent to two lines, trough two specific points?

R_Tweed — Mon, 23 Nov 2020 17:54:05 GMT

I would use a spline to draw your curve that is tangent at both ends at the indicated points. (screencast) . Although, in order to construct a "circle" that is tangent to both lines at specific points, the two points must have a perpendicular line that intersects at a line that bisects the angle of the two original lines.

Re: How to draw a circle tangent to two lines, trough two specific points?

dbroad — Mon, 23 Nov 2020 20:20:36 GMT

There can be no solution to the exact problem posed. In order for a "circle" to be tangent to be 2 straight lines, the points of tangency need to be "always" the same distance from the vertex formed by the two lines. Ask Kent has stated, there probably an infinite number of solutions involving ellipses.

Re: How to draw a circle tangent to two lines, trough two specific points?

leeminardi — Tue, 24 Nov 2020 03:26:57 GMT

I do not think that there are an infinite number of ellipses that will satisfy the requirement. One method to approximate the ellipse would be the following. Note, I would draw a picture but I'm away from my cad computer for a couple of days.Assume the two tangent points are labeled A and B. Divide the t uvwo line segments by 10 and draw lines from the 1st point on the line containing A to the 9th point of line with B. Then draw a line from the 2nd point of A to the 8th point of B. Repeat the pattern and the result should approximate an ellipse.

Another way to proceed is to create a spline as suggested. I would use the CV method and place a CV at A, then a CV at the intersection, and the 3rd and final CV at B. This would yield a degree 2 Bezier spline tangent to the 2 lines.

Re: How to draw a circle tangent to two lines, trough two specific points?

SEANT61 — Tue, 24 Nov 2020 06:00:35 GMT

This thread has evolved to a couple of sub-topics. Regarding an elliptical ‘fillet’, I agree with @Kent1Cooper that there are infinite elliptical arcs that could be tangent to those two points (infinite hyperbolic arcs as well if that were of any interest).

As pointed out by @leeminardi , a tan-int-tan degree 2 spline can create the blend as a Parabolic arc – and only one such parabola exists (Incidentally, the connection of division points approximates a parabola). An elliptical arc is created if the weight of the middle CP is reduced from 1.0. Hyperbolic results from a weight greater than 1.0.

In the attached drawing I modified a Degree 2 spline to create several examples. I use Lee Mac’s 5-Point Ellipse routine found here:

5-Point Ellipse | Lee Mac Programming (lee-mac.com)

and here

http://www.theswamp.org/index.php?topic=43859.msg491251#msg491251

Re: How to draw a circle tangent to two lines, trough two specific points?

SEANT61 — Tue, 24 Nov 2020 09:43:54 GMT

File

Re: How to draw a circle tangent to two lines, trough two specific points?

hak_vz — Tue, 24 Nov 2020 10:39:50 GMT

Circle option TTR or intersection of two perpendicular lines.

For ellipse consult this

Re: How to draw a circle tangent to two lines, trough two specific points?

hak_vz — Tue, 24 Nov 2020 10:41:31 GMT

Re: How to draw a circle tangent to two lines, trough two specific points?

Kent1Cooper — Tue, 24 Nov 2020 12:00:37 GMT

@hak_vz wrote:

....

For ellipse consult this

That seems to be about finding the unknown tangency points D1 and D2 from known point A to an already-existing Ellipse, and therefore finding unknown tangent lines t1 and t2. What the OP is trying to do is to find the Ellipse, starting from already having known Lines t1 and t2 and known point A and known points D1 and D2. That's a very different animal, and not just some kind of reversal of the process, since that webpage's approach requires knowing where the focal points of the Ellipse are, but of course in what the OP wants, those are unknown. [And they can't be known, since there are infinite solutions at different Ellipse aspect ratios.]

Re: How to draw a circle tangent to two lines, trough two specific points?

hak_vz — Tue, 24 Nov 2020 17:45:05 GMT

@Kent1CooperThis image is about general rules of tangents for ellipse. As you say there are infinite numbers of ellipses that can be constructed. If nearly symmetrical triangle is created with nearly equal distance P1A P2A it leads to Steiner inellipse.

When two tangents are orthogonal this two points can be taken as vertex end co-vertex of a ellipse and it leads to construction of ellipse with center point method, as you have shown in your previous post. When tangents are not orthogonal solution require complex calculations.

Re: How to draw a circle tangent to two lines, trough two specific points?

Anonymous — Fri, 27 Nov 2020 21:38:53 GMT

Thanks to everyone who answered! It seems I will either have to use an ellipse or parabola or change my design but all answers were great. I've learned a lot too.

Thanks a million!

Re: How to draw a circle tangent to two lines, trough two specific points?

stevor — Mon, 28 Dec 2020 22:37:16 GMT

For a circle, see about Apollonius, at cut-the-knot .

For an ellipse: 4 knowns, 2 pts, 2 slopes; maybe:

2x/aa - 2h/aa + y'2y/bb - y'2k/bb = 0

Re: How to draw a circle tangent to two lines, trough two specific points?

jayDB5 — Sat, 03 Jan 2026 19:03:20 GMT

If we adjust the constraints to have only one required point of tangency, then the solution can be found with the following:
1. Draw a circle with center at the intersection of the two lines and through the known/required point.

2. The circle's intersection with the other line is the desired tangent point on that line.
3. Draw a polyline with a line along the first line, then an arc with endpoint at the found intersection.