R.<m,n> = QQ[]
Ax=0
Ay=0
Bx=2
By=0
#m=tan half A
#n=tan half B
p=(1-m*n)/(m+n)
#I= incenter
#O=circumcenter
#H=orthocenter
Iy=2/(1/m+1/n)
Ix=Iy/m
#R= circumradius
#r=inradius
r=Iy
tanA=2*m/(1-m^2)
sinA=2*m/(1+m^2)
tanB=2*n/(1-n^2)
sinB=2*n/(1+n^2)
tanC=2*p/(1-p^2)
sinC=2*p/(1+p^2)
R=1/sinC
c=2
a=2*R*sinA
b=2*R*sinB
Cy=2/((1-m^2)/2/m+(1-n^2)/2/n)
Cx=Cy/2/m*(1-m^2)
Hx=Cx
Hy=Cx*(2-Cx)/Cy
Ox=1
Oy=(Cy-Hy)/2
print (a^2-(Bx-Cx)^2-(By-Cy)^2)
print (b^2-(Ax-Cx)^2-(Ay-Cy)^2)
print (R^2-(Ax-Ox)^2-(Ay-Oy)^2, R^2-(Bx-Ox)^2-(By-Oy)^2, R^2-(Cx-Ox)^2-(Cy-Oy)^2)
print (((Ix-Cx)*(Cy-Ay)+(Iy-Cy)*(Ax-Cx))/b/r, ((Ix-Cx)*(By-Cy)+(Iy-Cy)*(Cx-Bx))/a/r)
print ((Ax-Bx)*(Cx-Hx)+(Ay-By)*(Cy-Hy), (Bx-Cx)*(Ax-Hx)+(By-Cy)*(Ay-Hy), (Cx-Ax)*(Bx-Hx)+(Cy-Ay)*(By-Hy))
print (Cy^2-(a+b+c)*(a+b-c)*(b+c-a)*(c+a-b)/16)
print (c^2-a^2-b^2+2*a*b*sinC/tanC)