From: pnachtwey@gmail.com   
      
   There is a problem that Mathcad solves that Mathematica doesn't.  The problem   
   with the Mathcad solution is that it is too big to be useful in a real time   
   environment.   
      
   What I am trying to do is to find the center of a circle with radius R that is   
   tangent to two lines, line 0 and line 1.  I need to know the tangent points   
   too.  There are 6 equations and 6 unknowns.  I thought this would be simple.   
      
   There is the Mathematica problem:   
      
   In[132]:= eq1 = (yc-y0)^2+(xc-x0)^2==R^2     
   eq2 = (yc-y1)^2+(xc-x1)^2== R^2   
   eq3 = y0 == m0*x0+b0    
   eq4 = (yc-y0) == -(xc-x0)/m0    
   eq5 = y1 == m1*x1+ b1    
   eq6 =(yc-y1) == -(xc-x1)/m1    
   Out[132]= (-x0+xc)^2+(-y0+yc)^2==R^2   
   Out[133]= (-x1+xc)^2+(-y1+yc)^2==R^2   
   Out[134]= y0==b0+m0 x0   
   Out[135]= -y0+yc==(x0-xc)/m0   
   Out[136]= y1==b1+m1 x1   
   Out[137]= -y1+yc==(x1-xc)/m1   
   In[138]:= Solve[{eq1,eq2,eq3,eq4,eq5,eq6}{x0,y0,x1,y1,xc,yc}]   
   During evaluation of In[138]:= Solve::naqs: x0 ((-x0+xc)^2+(-y0+   
   c)^2==R^2)&&y0 ((-x1+xc)^2+(-y1+yc)^2==R^2)&&x1 (y0==b0+m0 x0)&&y1   
   (-y0+yc==(x0-xc)/m0)&&xc (y1==b1+m1 x1)&&yc (-y1+yc==(x1-xc)/m1) is not a   
   quantified system of equations and inequalities.    
   >>   
   Out[138]= Solve[{x0 ((-x0+xc)^2+(-y0+yc)^2==R^2),y0 ((-x1+xc)^2+   
   -y1+yc)^2==R^2),x1 (y0==b0+m0 x0),y1 (-y0+yc==(x0-xc)/m0),xc (y1==b1+m1 x1),yc   
   (-y1+yc==(x1-xc)/m1)}]   
      
   This is the error I get.   
   is not a quantified system of equations and inequalities   
      
   Thanks for having a look.   
      
   Peter Nachtwey   
      
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