How to find a circle tangent to two lines and passing through a point without (Tan Tan Tan)

[shahid.shaikh5FSSN]

Hello, 

I am trying to create a circle which is tangent to two lines and passing through a point. the only limitation is i cant use Autocad tan tan tan command. So how to construct this geometrically. Does any one have any other way than tangent command. 

Please see attached image for clarification. 

[imadHabash]

Hi,

i suggest to use Parametric Geometric options , it will help . >> Click << 

check it from your upper screen ribbon >> Parametric tab . 

[shahid.shaikh5FSSN]

Thanks for the reply...................its not about fixing the constrains rather than creating the geometry without using the tangent command.  

[parkr4st]

isn't that a 3 point circle?  CIRCLE            3P

[shahid.shaikh5FSSN]

Yes it is, i am trying to find tangent point geometrically not with the snap function. in other words you can say logic of tan tan tan function. 

[dbroad]

Assuming that you want to code the issue, look at this reference:

https://mathworld.wolfram.com/Circle-CircleIntersection.html#:~:text=The%20intersections%20of%20two%....

You would need to increase the radius of each reference circle by the radius of the circle to be drawn tangent to the two circles. The center point of the new circle would be at one of the two possible intersections.

If you just want a number of commands to do it, use the offset command twice and circle command once. I hope this isn't a request to answer a homework problem.

[shahid.shaikh5FSSN]

Thanks for the reply......yes i am trying to code the workflow in dynamo but having a difficulty in creating this circle. 

Thanks for the link but the link is not relevent, the radius of such circle will not be know in advance as you are trying to find out radius as well as center of such curve which will  be tangent to two lines/curve and passing through a point. 

 and yes i know the offset and radius method , its tan tan radius. what i am trying to do is tan tan tan is it possible with offset if radius is not known ?

[leeminardi · Accepted solution]

I would take a numerical approach. I assume you meant circles and not "lines" in your problem statement and that you want to create a circle that is tangent to both circle and passes through a point.

Assume one of the circles is c1 with a radius r1 and the other circle is c2 with radius r2 and the point is p.

Make a guess for r, the radius of the circle you wish to define.  Define a circle c1a concentric to c1 that has a radius r1 + r and define another circle c2a concentric to c2 with a radius r2 + r.  Find the intersection of the these two circles that is closest to p. This is the center of the first guess of a circle that is tangent to the 2 circle and passes through p. Now find the distance from p to the center of the new circle.  If the distance is less than r increase the value of r and repeat. If it is greater than r decrease the value of r and repeat. You can structure the loop to halve the change in r for each iteration. When I have a few minutes I can program this logic in vlisp if you wish.  Note, I would use a numerical approach to find the intersection of the 2 circles but you can also do it analytically.  

I'm not sure what would be a good initial guess for r but I would try something like the larger of these two calculations:

1.  distance from c1 center to (p - r1)

2. distance from c2 center to (p - r2)

I think the calculation would converge quickly.

[shahid.shaikh5FSSN]

Thanks alot for the logic......yes this is what i was looking for. Will work along this logic and see if it works. 

yes one side i have curve and other side it may vary between line and curve but with this logic i can try and find the solution. 

cheers, and thanks 

Shahid Shaikh