Calculating the points of tangency for two circles given a picture

[arashmobilebo]

I have two circles with the same radius and I want to calculate the points of tangency.
For example, in the picture below, I want to calculate [FONT=MathJax_Main]([FONT=MathJax_Math]x[FONT=MathJax_Main]3[FONT=MathJax_Main],[FONT=MathJax_Math]y[FONT=MathJax_Main]3[FONT=MathJax_Main]) and [FONT=MathJax_Main]([FONT=MathJax_Math]x[FONT=MathJax_Main]4[FONT=MathJax_Main],[FONT=MathJax_Math]y[FONT=MathJax_Main]4[FONT=MathJax_Main]). I have the radius and the distance between the two circles as shown below:

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[Villyer]

What can be said about the angle between a radius and the tangent line that it touches?

 

[LCKurtz]

You can calculate the vector $\vec D$ between the centers. Can you make a vector perpendicular to it the radius units long to get from the centers to the tangent points?

 

[arashmobilebo]

Can you make a vector perpendicular to it the radius units long to get from the centers to the tangent points?

thanks,can you explain me more about what should i do?

 

[arashmobilebo]

What can be said about the angle between a radius and the tangent line that it touches?

i think they are Perpendicular

 

[LCKurtz]

You can calculate the vector $\vec D$ between the centers. Can you make a vector perpendicular to it the radius units long to get from the centers to the tangent points?

thanks,can you explain me more about what should i do?

I think I just told you. Do you understand vectors? Can you calculate $\vec D\,$? Do you know how to make a perpendicular vector?

You have to show some effort.

 

[arashmobilebo]

I think I just told you. Do you understand vectors? Can you calculate $\vec D\,$? Do you know how to make a perpendicular vector?

You have to show some effort.

Yes I know them!

 

[Villyer]

i think they are Perpendicular

They are.

So consider just the quadrilateral formed by the tangent line, the line connecting the centers, and the two radii that touch the tangent segment.

You know two ends of this figure (the centers of the circles), and the other two points are the two you are interested in.

If you identiy what type of quadrilateral it is, finding the last two points shouldn't be that hard.

 

[arashmobilebo]

thanks,here i got my answer:

http://math.stackexchange.com/quest...s-of-tangency-for-two-circles-given-a-picture

 

[Villyer]

That looks like where you got the problem from. Do you understand the work that they did?

 

[arashmobilebo]

That looks like where you got the problem from. Do you understand the work that they did?

i asked the question there.yes i got it