"PONCELET 2. Experimentando."

"Se tiene la circunferencia unidad y la circunferencia de centro (à,0) y radi~
o r (suficientemente grande)"

"Se escoge el punto (cost, sint) y se obtiene la tangente y los dos puntos de~
 interseccion con la exterior"

(x-alpha)^2+y^2=r^2

(y-SIN(t))*TAN(t)+x-COS(t)=0

PUNTOPOSCORRAT(alpha,r,t):=IF(DET([[0,0,1],[SIN(t)*SQRT(-alpha^2*COS(t)^2+2*a~
lpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,-COS(t)*SQRT(-alpha^2*COS(t)^2+2*alp~
ha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t),1],[-SIN(t)*SQRT(-alpha^2*COS(t)^~
2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,COS(t)*SQRT(-alpha^2*COS(t)^2+2~
*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t),1]])>0,[SIN(t)*SQRT(-alpha^2*~
COS(t)^2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,-COS(t)*SQRT(-alpha^2*CO~
S(t)^2+2*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t)],[-SIN(t)*SQRT(-alpha~
^2*COS(t)^2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,COS(t)*SQRT(-alpha^2*~
COS(t)^2+2*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t)])

PUNTONEGCORRAT(alpha,r,t):=IF(DET([[0,0,1],[SIN(t)*SQRT(-alpha^2*COS(t)^2+2*a~
lpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,-COS(t)*SQRT(-alpha^2*COS(t)^2+2*alp~
ha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t),1],[-SIN(t)*SQRT(-alpha^2*COS(t)^~
2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,COS(t)*SQRT(-alpha^2*COS(t)^2+2~
*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t),1]])>0,[-SIN(t)*SQRT(-alpha^2~
*COS(t)^2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,COS(t)*SQRT(-alpha^2*CO~
S(t)^2+2*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t)],[SIN(t)*SQRT(-alpha^~
2*COS(t)^2+2*alpha*COS(t)+r^2-1)+COS(t)+alpha*SIN(t)^2,-COS(t)*SQRT(-alpha^2*~
COS(t)^2+2*alpha*COS(t)+r^2-1)-alpha*SIN(t)*COS(t)+SIN(t)])

MACROTANGENTE(alpha,r,t):=[x^2+y^2-1=0,(x-alpha)^2+y^2=r^2,[COS(t),SIN(t)],[P~
UNTOPOSCORRAT(alpha,r,t),PUNTONEGCORRAT(alpha,r,t)]]

"**********************************"

"EXPERIMENTOS"

MACROTANGENTE(2,5,1)

MACROTANGENTE(3,6,2)