# Tangent to several circles

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### Tangent to several circles

Dear Math Teacher;
I work in Rock Mechanics and we have a standard methodology of description of State of Stress called Mohr Circle... It is basically a series of circles with their centers lying on the X axis and having various radius. A rock Mechanics Parameter called MOHR ENVELOP is a curve (most probably a Hyperbola) that is tangent to all those circles... 'm trying to find th equations of such a Hyperbola that would TANGENT to such several circles... any clue? (I was able to extract and apply (on Mathematica) the equation of a line that is tangent to two circles)

Thank you

Yasser
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### Re: Tangent to several circles

Hello,

When should you be ready?
At this point, I work on other very urgent orders.
Please, send me more details.
I will try to help.

e-mail: wml@abv.bg

V. Lishkov
Guest

### Re: Tangent to several circles

Thank you...
Pls find below the description of the problem in mathematical format:
Suppose that I have three circles:
Circle 1: {95,0}, radius: 105
Circle2: {350,0}, radius: 170
Circle3: {700,0}, radius: 230

in Rock Mechanics, those circles represent states of stresses at various points and various conditions, and we know that the ENVELOP to those circles constitute what we call Mohr Envelop (a Curve that is most probable a Hyperbola, and that is Tangent to ALL circles)

So the problem is: how to find mathematically the equation of that Envelop (hyperbola that is tangent to all three circles)...

Thank you in advance

Yasser
Guest

### Re: Tangent to several circles

See the attachment below, please:
Attachments Untitled.png (13.05 KiB) Viewed 1621 times

Math Tutor

Posts: 405
Joined: Sun Oct 09, 2005 11:37 am
Reputation: 26

### Re: Tangent to several circles

center point, X=1113.5235 Y=-3377.8355 Z= 0.0000
Guest

### Re: Tangent to several circles

This is EXACTELY what I want, but I want it as a Mathematical Formula (I use Mathematica 8.1 to generate the circles out of a state of stress and would like to generate also the Hyperbola out of a mathematical formula, so I may use it for further processing: Differentiation, integration, state of stress comparisons, etc.)...
Thank you in Advance

Yasser
Guest

### Re: Tangent to several circles

well
I'll see to bring out some form or system
maybe tomorrow
Guest

### Re: Tangent to several circles

Here is the result from Mr. Lishkov
A system of 3 equations in 3 variables.
Attachments Points.docx

Math Tutor

Posts: 405
Joined: Sun Oct 09, 2005 11:37 am
Reputation: 26

### Re: Tangent to several circles

must be solved first system of three equations
The second is not true
Guest

### Re: Tangent to several circles

The file is updated by Mr. Lishkov
Attachments Points.docx

Math Tutor