# Question:Euler’s circle of an inscribed quadrilateral

## Question:Euler’s circle of an inscribed quadrilateral

Maple 2021

restart;
with(geometry):
with(plots):
_EnvHorizont:lName = 'x';
_EnvVerticalName = 'y';
Vdot := proc(U, V) local i; add(U[i]*V[i], i = 1 .. 2); end proc;
R := 5;
ang := [3/4*Pi, -(3*Pi)/4, -Pi/6,4*Pi/9];
seq(point(`||`(P, i), [R*cos(ang[i]), R*sin(ang[i])]), i = 1 .. 4);
pts:=[seq(P || i,i=1..4)]:
seq(dsegment(`||`(seg, i), [`||`(P, i), `||`(P, irem(i, 4) + 1)]), i = 1 .. 4);
Triangle(Tr1,[P1,P2,P4]);
EulerCircle(Elc1,Tr1,'centername'=o);
circle(cir, [point(OO, [0, 0]), R]);
dist := proc(M, N) sqrt(Vdot(M - N, M - N)); end proc;
display(draw([P1(color = black, symbol = solidcircle, symbolsize = 12),
P2(color = black, symbol = solidcircle, symbolsize = 12),
P3(color = black, symbol = solidcircle, symbolsize = 12),
P4(color = black, symbol = solidcircle, symbolsize = 12),seg1,
seg2,seg3,seq4,Tr1,Elc1,
cir(color = blue)]),
textplot([[seq( [ coordinates(`||`(P, i))[], convert(`||`(P, i), string)],i=1..4],
,align = [above, right]), axes = none);
does not recognize neg4 or tr1? I don't know to manage. Thank you.

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