# Homework Help: Calculating the points of tangency for two circles given a picture

1. Jul 14, 2012

### 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][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main])[/FONT] and [FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]y[/FONT][FONT=MathJax_Main]4[/FONT][FONT=MathJax_Main])[/FONT]. I have the radius and the distance between the two circles as shown below:[/FONT]

2. Jul 14, 2012

### Villyer

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

3. Jul 14, 2012

### 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?

4. Jul 15, 2012

### arashmobilebo

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

5. Jul 15, 2012

### arashmobilebo

i think they are Perpendicular

6. Jul 15, 2012

### LCKurtz

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.

7. Jul 15, 2012

### arashmobilebo

Yes I know them!

8. Jul 15, 2012

### Villyer

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.

9. Jul 15, 2012

### arashmobilebo

10. Jul 15, 2012

### Villyer

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

11. Jul 15, 2012

### arashmobilebo

i asked the question there.yes i got it