Question:Chevron's lemma

Question:Chevron's lemma

Maple 2021

restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':
_EnvVerticalName = 'y':
EQ := proc(M, N)
local eq, sol;
eq := simplify(expand((y - M[2])/(x - M[1]) - (N[2] - M[2])/(N[1] - M[1])));
sol := solve(eq, y);
RETURN(y = sol); end proc:
_local(D);
point(A, [-2, 7]):
point(B, [-5, -2]):
point(C, [8, -7]):
point(E, [1, 4]):
EQ([-5, -2], [8, -7]):
point(D, [1, subs(x = 1, rhs(%))]):
BD := distance(B, D):
DC := distance(C, D):
triangle(ABC, [A, B, C]):
area(ABC):
triangle(ABD, [A, B, D]):
area(ABD):
triangle(EBD, [E, B, D]):
area(EBD):
triangle(EDC, [E, D, C]):
area(EDC):
triangle(AEC, [A, E, C]):
area(AEC):
triangle(ABE, [A, B, E]):
area(ABE):
is(area(ABE)/area(AEC) = BD/DC):
display*([draw*[A(color = black, symbol = solidcircle, symbolsize = 6),
B(color = black, symbol = solidcircle, symbolsize = 6),
C(color = black, symbol = solidcircle, symbolsize = 6),
ABC(color = blue)],
textplot*([[coordinates(A)[], "A"],
[coordinates(B)[], "B"],
[coordinates(C)[], "C3"]],
align = [above, right])],
axes = none,
title = "Lemme du Chevron");
The program simply reproduces display...Why; Thank you.
display*([draw*[A(color = black, symbol = solidcircle, symbolsize = 12), B(color = black, symbol = solidcircle, symbolsize = 12), C(color = black, symbol = solidcircle, symbolsize = 12), ABC(color = blue)], textplot*([[-2, 7, "A"], [-5, -2, "B"], [8, -7, "C3"]], align = [above, right])], axes = none, title = "Lemme du Chevron")

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