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Question 878593: First post
Hello, for my artificial intelligence I'm programming I need to figure out a location thats called by a math formula I just can't find.
I realise this is something hard to ask and I hope someone can solve it since even my math tutor can't.
There's ttwo circles and 1 point located in a coordinate system
For the sake of explaining the problem, let's callthem circle A,B and point C
We can assume that:
-circle A's radius is always bigger than B
-there will never be 2 of the points at the exact same location
-the radius for A and B are variables
Now I need to calculate the point where A has to placed so that:
- the middle of circle B is in the circle of A
- the middle of circle A is NOT in the circle of B
- I need the point that's as far away as possible from point C
First answer
Your explanation is confusing, here's what I've got so far.
You're given two radii: R%5BA%5D and R%5BB%5D, which can be variables.
Circles A and B cannot overlap. I think that's what you mean by "middle".
I'm guessing you're given the location of circle A's center.
Then you have to calculate a possible location for circle B's center.
That's straightforward. You can find a zone to place circle B's center so that it doesn't overlap circle A.
Now what is the relationship between point C and the centers of the two circles. Does the center of B have to be the maximum distance from point C?
So you're given the coordinates of circle A center(x%5BA%5D,y%5BA%5D), circle A radiusR%5BA%5D, circle B radiusR%5BB%5D, coordinates of C(x%5BC%5D,y%5BC%5D),, and you have to find the maximum distance from the center of circle B to point C within some bounded plane?
Further explanation :
Sorry, I actually failed to include what I was actually looking for:
I'm looking for a point where I can move the center of circle A to(with some requirements).
further info :
The location of the center of circle B is set (for example (10,20))
the radius of circle B is known (for example : 2)
the radius of circle A is known and always bigger than the radius of circle B (for example : 3)
the location of point C is known (for example (15,25)
The requirements :
- the center of circle B is in the circle drawn by the center and radius of A
- the center of circle A is NOT in the circle drawn by the center and radius of B
- I need to move the center of A as far away as possible from point C without breaking the other 2 requirements.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! 
OK, I think I get it now.
The blue circle is circle B.
The green circle is circle A.
The dot is C.
The green circle is located at the maximum distance from C while still capturing the center of circle B along its circumference.
Once you know the location of C and circle B, you know the direction of the center of circle A because the three points are collinear.
The maximum distance is then the distance from C to center of B plus the radius of B plus the radius of A.
You can email me to verify that this is the correct setup and then we can work on a solution.
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