Circle Tangent to a Circle

[zarkrid]

Hello, I have this problem:

I want the big circle to be tangent to the small circle and the rotation base point of the big circle is the upper arc point. Does anyone know how I can do it?

Thanks.

[TheCADnoob · Accepted solution]

I did it with parametric constraints. just added a point and locked it and the other circle then made the point coincident with the circle and then made the diameters set. After that i rotated the circle and then made the two circles tangent using the tangent constraint. 

I also used another method which seems to work but i couldn't find any notes on it to prove that is worked. I wold recommend using the parametric method without proof for the second method. 

[leeminardi]

Not done!

[zarkrid]

That is exactly how I wanted it to be. Thank you very much, sir!

[leeminardi · Accepted solution]

Here's a geometric construction process that doesn't require parametrics in case you are interested.

1. Construct the red circle with a radius = large radius - small radius centered at the small circle.
2. Construct the cyan circle with a radius = large circle centered at the point on the large circle.
3. Use align (I prefer it to rotate) using points 1, 2, 3 (the center of the original large circle) and 4 (the intersection of the red and cyan circles.

Command: ALIGN
Select objects: 1 found
Select objects:
Specify first source point:  #1
Specify first destination point:  #2
Specify second source point: #3
Specify second destination point #4:
Specify third source point or <continue>: [Enter]
Scale objects based on alignment points? [Yes/No] <N>: N 

[zarkrid]

This is working perfect too.

Thank you, sir!

[TheCADnoob]

In the spirit of beating a dead horse, i thought of another method on the commute this morning. 

You can us the Law of Cosins SSS

https://www.varsitytutors.com/precalculus-help/solve-a-triangle-in-which-3-sides-are-given-sss

The three sides of the triangle are defined by the given length (g) between the small circle and the rotation point, the length of the intersection point to the center of the big circle (r2) and the length from the center of the small circle to the center of the big circle (r2+r1) with these valuse you can solve for the angle A. once you have that angle you can rotate a lint the length of (r1+r2) away from the given line g. Then you can place a circle at the endpoint of (r1+r2). 

[zarkrid]

This method is really amazing. I would never have thought of that way. Thank you for all your help.

From pure curiosity, how did you think about this formula to solve this problem?

[leeminardi]

@TheCADnoob clever!  It is essentially the mathematical approach to the solution I took graphically but you chose the "upper"of the two solutions (for point #4 in my post use the upper intersection of the cyan and red circles).

[TheCADnoob]

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@zarkrid wrote:

From pure curiosity, how did you think about this formula to solve this problem?

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I was trying to think of a way to prove the validity of my second method ( the non parametric method ) in the video. I realized that the pivot point on the big circle would be the same length of the radius of the big circle and that the tangent to tangent radius were just r1 and r2 and that the distance from the small circle to the pivot point was static which gives you Three sides of a triangle. With that you could use the SSS method to get the offset angle and then you just put the circle at the end of the line rotated by that angle. So basically i found that method when proving my other method to my self. (at least i think haha, Id still get a professionals opinion)