Find the point of contact of the common tangent of two circles (sympy matrix)

Please tell me how to use python functions, arguments and return values. It would be helpful if you could tell us the recommended reference page. I think it will be shorter. Thank you.

"Only when they are far apart ... 4 tangents" By the way, the following program calculates only one The size of r1r2 may be relevant. It is assumed that r1 <r2.

(Reference) Find the common tangent of two circles https://qiita.com/tydesign/items/0100c49c6335695e6990


#[Example] Center(10,12)Radius 2 and center(50,42)Find the common tangent of a circle with a radius of 30
from sympy import *																													
var('x1 y1 r1 x2 y2 r2 tx ty co si sx1 sy1 sx2 sy2')																													
sx1=0																													
sy1=r1																													
sx2=sqrt((x1-x2)**2+(y1-y2)**2-(r2-r1)**2)																													
sy2=r2																													
v=solve([co*sx1-si*sy1+tx-x1,																													
              si*sx1+co*sy1+ty-y1,																													
              co*sx2-si*sy2+tx-x2,																													
              si*sx2+co*sy2+ty-y2],																													
             [co,si,tx,ty])																													
A=Matrix([																													
           [v[co],-v[si],v[tx]],																													
           [v[si], v[co],v[ty]],																													
           [    0,       0,    1]																													
])																													
B=Matrix([																													
          [sx2],																													
          [  0] ,																													
          [  1]																													
])																													
AB=A*B																													
print("---------------------------------------")																													
print(tx)																													
print(ty)																													
print(AB[0])																													
print(AB[1])																													
print("---------------------------------------")																													
print(v[tx].subs({x1:10,y1:12,r1:2,x2:50,y2:42,r2:32}),																													
v[ty].subs({x1:10,y1:12,r1:2,x2:50,y2:42,r2:32}))																													
print(AB[0].subs({x1:10,y1:12,r1:2,x2:50,y2:42,r2:32}),																													
AB[1].subs({x1:10,y1:12,r1:2,x2:50,y2:42,r2:32}))#

Omitted in the middle of the result 10 10 50 10

The tangent equation is (not yet)

I feel that the method of intersection in class is fast. (Not yet)

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