The Butterfly Theorem

Butterfly:=proc() local P,t,i,R,L,M,X,Y,O:

for i from 1 to 4 do   P[i]:= ParamCircle (  O,R,t[i]   )   od:

M:=PtLe(P[1],P[3])   ,   Le (P[2],P[4])  ):   L:=PerpPQ(O,M):

X:=Pt ( Le(P[1],P[4])   ,   L):   Y:=Pt ( Le(P[2],P[3])   ,   L ):

ItIsZero(   DeSq(M,X)   -  DeSq(M,Y)   ):

end:


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