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

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

"CIRCUNCIRCULO Y CIRCULO DE FEUERBACH"

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

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

"UNAS CUANTAS FUNCIONES BASICAS AUXILIARES"

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

PMEDIO(a,b,c,d):=[(a+c)/2,(b+d)/2]

PUNTOMEDIOV(a,b):=(a+b)/2

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

RECTAPORDOSPUNTOS(a,b,c,d):=x*(b-d)+y*(c-a)+a*d-b*c=0

RECTAPORDOSPUNTOSV(u,v):=x*(u SUB 2-v SUB 2)+y*(v SUB 1-u SUB 1)+u SUB 1*v SU~
B 2-u SUB 2*v SUB 1=0

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

INTERSECCIONRECTAS(alpha,beta,tau,kappa,lambda,mu):=[(beta*mu-tau*lambda)/(al~
pha*lambda-beta*kappa),(tau*kappa-alpha*mu)/(alpha*lambda-beta*kappa)]

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

RECTAPARALELA(m,n,p,a,b):=m*(x-a)+n*(y-b)=0

RECTAPARALELAV(m,n,p,v):=m*(x-v SUB 1)+n*(y-v SUB 2)=0

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

RECTAPERPENDICULAR(m,n,p,a,b):=n*(x-a)-m*(y-b)=0

RECTAPERPENDICULARV(m,n,p,v):=n*(x-v SUB 1)-m*(y-v SUB 2)=0

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

RECTAPENDIENTEARECTACART(a,b,m):=IF(m=inf,x=a,m*x-y-m*a+b=0)

RECTAPENDIENTEARECTACARTV(a,m):=IF(m=inf,x=a SUB 1,m*x-y-m*a SUB 1+a SUB 2=0)

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

RECTACARTAPUNTOPENDIENTE(m,n,p):=IF(n/=0,SOLVE(m*x+n*y+p=0,y),SOLVE(m*x+n*y+p~
=0,x))

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

MEDIATRIZ(a,b,c,d):=2*x*(a-c)+2*y*(b-d)-a^2-b^2+c^2+d^2=0

MEDIATRIZV(a,b):=(b-a) SUB 1*(x-((a+b)/2) SUB 1)+(b-a) SUB 2*(y-((a+b)/2) SUB~
 2)=0

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

INTERSECDIAGCUADR(m,n,p,q,r,s,t,u):=[(m*(p*(s-u)+t*(q-s))-r*(n*(p-t)-p*u+q*t)~
)/(m*(q-u)+n*(t-p)+p*s-q*r+r*u-s*t),(m*s*(q-u)-n*(p*u+q*(r-t)-r*u)+s*(p*u-q*t~
))/(m*(q-u)+n*(t-p)+p*s-q*r+r*u-s*t)]

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

NORMALUNITARIA(a,b,m,n,p):=IF(m*a+n*b+p>0,-1/(m^2+n^2)^(1/2)*[m,n],1/(m^2+n^2~
)^(1/2)*[m,n])

NORMALUNITARIAV(v,m,n,p):=IF(m*v SUB 1+n*v SUB 2+p>0,-1/(m^2+n^2)^(1/2)*[m,n]~
,1/(m^2+n^2)^(1/2)*[m,n])

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

DISTANCIA(a,b,m,n,p):=ABS(m*a+n*b+p)/(m^2+n^2)^(1/2)

DISTANCIAV(v,m,n,p):=ABS(m*v SUB 1+n*v SUB 2+p)/(m^2+n^2)^(1/2)

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

SIMETRICO(a,b,m,n,p):=[a,b]+2*DISTANCIA(a,b,m,n,p)*NORMALUNITARIA(a,b,m,n,p)

SIMETRICOV(v,m,n,p):=v+2*DISTANCIAV(v,m,n,p)*NORMALUNITARIAV(v,m,n,p)

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

SIMETRICODEPUNTORESPECTOPUNTO(a,b,p,q):=2*[p,q]-[a,b]

SIMETRICODEPUNTORESPECTOPUNTOV(v,p):=2*p-v

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

SIMETRICOPUNTORESPECTORECTA(a,b,m,n,p):=[(a*(n^2-m^2)-2*b*m*n-2*p*m)/(m^2+n^2~
),(b*(m^2-n^2)-2*a*m*n-2*p*n)/(m^2+n^2)]

SIMETRICOPUNTORESPECTORECTAV(v,m,n,p):=[(v SUB 1*(n^2-m^2)-2*v SUB 2*m*n-2*p*~
m)/(m^2+n^2),(v SUB 2*(m^2-n^2)-2*v SUB 1*m*n-2*p*n)/(m^2+n^2)]

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

ROTACION(a,b,p,q,ang):=[p,q]+[(a-p)*COS(ang)-(b-q)*SIN(ang),(a-p)*SIN(ang)+(b~
-q)*COS(ang)]

ROTACION(v,p,ang):=p+[(v SUB 1-p SUB 1)*COS(ang)-(v SUB 2-p SUB 2)*SIN(ang),(~
v SUB 1-p SUB 1)*SIN(ang)+(v SUB 2-p SUB 2)*COS(ang)]

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

HOMOTETICODEVRESPECTOPRAZONK(u,v,p,q,k):=[p,q]+k*[u-p,v-q]

HOMOTETICODEVRESPECTOPRAZONKV(v,p,k):=p+k*(v-p)

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

INVERSODEVRESPECTOPPOTENCIAK(u,v,p,q,k):=[p,q]+k/ABS([u-p,v-q])^2*[u-p,v-q]

INVERSODEVRESPECTOPPOTENCIAKV(v,p,k):=p+k/ABS(v-p)^2*(v-p)

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

TRIANGULO(m,n,p,q,r,s):=[[m,n],[p,q],[r,s],[m,n]]

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

"EXPERIMENTANDO CON LAS MEDIANAS"

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

MEDIANAATRIANGULO(m,n,p,q,r,s):=RECTAPORDOSPUNTOS(m,n,(p+r)/2,(q+s)/2)

MEDIANABTRIANGULO(m,n,p,q,r,s):=MEDIANAATRIANGULO(p,q,r,s,m,n)

MEDIANACTRIANGULO(m,n,p,q,r,s):=MEDIANAATRIANGULO(r,s,m,n,p,q)

MACROMEDIANASTRIANGULO(m,n,p,q,r,s):=[[[m,n],[p,q],[r,s],[m,n]],[MEDIANAATRIA~
NGULO(m,n,p,q,r,s),MEDIANABTRIANGULO(m,n,p,q,r,s),MEDIANACTRIANGULO(m,n,p,q,r~
,s)]]

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

MACROMEDIANASTRIANGULO(3,4,-2,5,6,1)

MACROMEDIANASTRIANGULO(0,4,-2,-3,5,2)

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

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

BARICENTROTRIANGULO(m,n,p,q,r,s):=[(m+p+r)/3,(n+q+s)/3]

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

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

"EXPERIMENTANDO CON LAS ALTURAS DE UN TRIANGULO"

ALTURAATRIANGULO(m,n,p,q,r,s):=x*(r-p)+y*(s-q)+m*(p-r)+n*(q-s)=0

ALTURABTRIANGULO(m,n,p,q,r,s):=ALTURAATRIANGULO(p,q,r,s,m,n)

ALTURACTRIANGULO(m,n,p,q,r,s):=ALTURAATRIANGULO(r,s,m,n,p,q)

MACROALTURASTRIANGULO(m,n,p,q,r,s):=[[[m,n],[p,q],[r,s],[m,n]],[ALTURAATRIANG~
ULO(m,n,p,q,r,s),ALTURABTRIANGULO(m,n,p,q,r,s),ALTURACTRIANGULO(m,n,p,q,r,s)]~
]

MACROALTURASTRIANGULO(0,0,4,0,1,2)

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

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

ORTOCENTROTRIANGULO(m,n,p,q,r,s):=[-(m*(n*(p-r)-p*q+r*s)+(n^2-n*(q+s)+p*r+q*s~
)*(q-s))/(m*(q-s)+n*(r-p)+p*s-q*r),(m^2*(p-r)+m*(n*(q-s)-p^2+r^2)+n*(r*s-p*q)~
+p^2*r+p*(q*s-r^2)-q*r*s)/(m*(q-s)+n*(r-p)+p*s-q*r)]

ORTOCENTROTRIANGULO(0,0,4,0,1,2)

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

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

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

"EXPERIMENTANDO CON LAS MEDIATRICES"

MEDIATRIZATRIANGULO(m,n,p,q,r,s):=MEDIATRIZ(p,q,r,s)

MEDIATRIZBTRIANGULO(m,n,p,q,r,s):=MEDIATRIZATRIANGULO(p,q,m,n,r,s)

MEDIATRIZCTRIANGULO(m,n,p,q,r,s):=MEDIATRIZATRIANGULO(r,s,m,n,p,q)

MACROMEDIATRICESTRIANGULO(m,n,p,q,r,s):=[[[m,n],[p,q],[r,s],[m,n]],[MEDIATRIZ~
ATRIANGULO(m,n,p,q,r,s),MEDIATRIZBTRIANGULO(m,n,p,q,r,s),MEDIATRIZCTRIANGULO(~
m,n,p,q,r,s)]]

MACROMEDIATRICESTRIANGULO(0,0,4,0,2,1)

CIRCUNCENTROTRIANGULO(m,n,p,q,r,s):=[0.5*(m^2*(q-s)+n^2*(q-s)-n*(p^2+q^2-r^2-~
s^2)+p^2*s+q*(q*s-r^2-s^2))/(m*(q-s)+n*(r-p)+p*s-q*r),-0.5*(m^2*(p-r)-m*(p^2+~
q^2-r^2-s^2)+n^2*(p-r)+p^2*r-p*(r^2+s^2)+q^2*r)/(m*(q-s)+n*(r-p)+p*s-q*r)]

CIRCUNCENTROTRIANGULO(0,0,4,0,2,1)

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

CIRCUNCIRCULO(m,n,p,q,r,s):=(x-(CIRCUNCENTROTRIANGULO(m,n,p,q,r,s)) SUB 1)^2+~
(y-(CIRCUNCENTROTRIANGULO(m,n,p,q,r,s)) SUB 2)^2-ABS(CIRCUNCENTROTRIANGULO(m,~
n,p,q,r,s)-[m,n])^2=0

CIRCUNCIRCULO(0,0,4,0,2,1)

MACROCIRCUNCIRCULOTRIANGULO(m,n,p,q,r,s):=[[[m,n],[p,q],[r,s],[m,n]],CIRCUNCI~
RCULO(m,n,p,q,r,s),CIRCUNCENTROTRIANGULO(m,n,p,q,r,s)]

MACROCIRCUNCIRCULOTRIANGULO(0,0,4,0,2,1)

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

MACROCIRCULOFEUERBACHTRIANGULO(m,n,p,q,r,s):=[TRIANGULO(m,n,p,q,r,s),CIRCUNCI~
RCULO(m,n,p,q,r,s),CIRCUNCIRCULO((m+p)/2,(n+q)/2,(p+r)/2,(q+s)/2,(m+r)/2,(n+s~
)/2)]

MACROCIRCULOFEUERBACHTRIANGULO(0,0,4,0,3,2)

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