"Aqui esta la demostracion general del teorema de Feuerbach con cuentas de tr~
igo"

"Mirar los papeles de Feurbach del 21 Agosto 98"

Trigonometry:=Expand

;Simp(User)
(SIN(a)^2*(SIN(t)^2+2*(r+1)*SIN(t)+r^2+2*r+1)-SIN(a)*(2*SIN(t)^2+4*(r+1)*SIN(~
t)+2*(r+1)^2)+SIN(t)^2+2*(r+1)*SIN(t)+(r+1)^2)/COS(a)^2+SIN(a)*(SIN(t)+1)-SIN~
(t)-1

COS(t)*(SIN(a)-SIN(t))/(COS(t)+SIN((a-t)/2)+COS((a+t)/2))

FACTOR((SIN(a)^2*(SIN(t)^2+2*(r+1)*SIN(t)+r^2+2*r+1)-SIN(a)*(2*SIN(t)^2+4*(r+~
1)*SIN(t)+2*(r+1)^2)+SIN(t)^2+2*(r+1)*SIN(t)+(r+1)^2)/COS(a)^2+SIN(a)*(SIN(t)~
+1)-SIN(t)-1,Rational,a,r,t)

;Simp(#6)
(SIN(a)-1)*(COS(a)^2*(SIN(t)+1)+SIN(a)*(SIN(t)^2+2*(r+1)*SIN(t)+(r+1)^2)-SIN(~
t)^2-2*(r+1)*SIN(t)-(r+1)^2)/COS(a)^2

(SIN(a)-1)*(COS(a)^2*(SIN(t)+1)+SIN(a)*(SIN(t)^2+2*(r+1)*SIN(t)+(r+1)^2)-SIN(~
t)^2-2*(r+1)*SIN(t)-(r+1)^2)

;Sub(#8)
(SIN(a)-1)*(COS(a)^2*(SIN(t)+1)+SIN(a)*(SIN(t)^2+2*(COS(t)*(SIN(a)-SIN(t))/(C~
OS(t)+SIN((a-t)/2)+COS((a+t)/2))+1)*SIN(t)+(COS(t)*(SIN(a)-SIN(t))/(COS(t)+SI~
N((a-t)/2)+COS((a+t)/2))+1)^2)-SIN(t)^2-2*(COS(t)*(SIN(a)-SIN(t))/(COS(t)+SIN~
((a-t)/2)+COS((a+t)/2))+1)*SIN(t)-(COS(t)*(SIN(a)-SIN(t))/(COS(t)+SIN((a-t)/2~
)+COS((a+t)/2))+1)^2)

;Simp(#9)
(2*COS(t)*COS(a/2)*(COS(a)^2+(SIN(a)+1)*(SIN(a)-1))*(SIN(t)+1)*(COS(t/2)-SIN(~
t/2))+2*COS(t)*SIN(a/2)*(COS(a)^2+(SIN(a)+1)*(SIN(a)-1))*(SIN(t)+1)*(COS(t/2)~
-SIN(t/2))+COS(a)^2*(SIN(t)+1)*(SIN(a)*(COS(t/2)-SIN(t/2))^2+COS(t)^2-SIN(t)+~
1)+(SIN(a)-1)*(SIN(a)^2*COS(t)^2+SIN(a)*(SIN(t)^2*(COS(t/2)-SIN(t/2))^2+4*COS~
(t)^2+SIN(t)-1)+COS(t)^2*(SIN(t)^2-(SIN(t)+1)*(SIN(t)-1))+(1-SIN(t))*(SIN(t)^~
2+2*SIN(t)+1)))*(SIN(a)-1)/(COS(a/2)*(COS(t/2)-SIN(t/2))+SIN(a/2)*(COS(t/2)-S~
IN(t/2))+COS(t))^2

(2*COS(t)*COS(a/2)*(COS(a)^2+(SIN(a)+1)*(SIN(a)-1))*(SIN(t)+1)*(COS(t/2)-SIN(~
t/2))+2*COS(t)*SIN(a/2)*(COS(a)^2+(SIN(a)+1)*(SIN(a)-1))*(SIN(t)+1)*(COS(t/2)~
-SIN(t/2))+COS(a)^2*(SIN(t)+1)*(SIN(a)*(COS(t/2)-SIN(t/2))^2+COS(t)^2-SIN(t)+~
1)+(SIN(a)-1)*(SIN(a)^2*COS(t)^2+SIN(a)*(SIN(t)^2*(COS(t/2)-SIN(t/2))^2+4*COS~
(t)^2+SIN(t)-1)+COS(t)^2*(SIN(t)^2-(SIN(t)+1)*(SIN(t)-1))+(1-SIN(t))*(SIN(t)^~
2+2*SIN(t)+1)))*(SIN(a)-1)

;Simp(#11)
0