% Eukleides example
A B C triangle
draw(A, B, C)

D= midpoint(segment(A,B))
draw(segment(C,D), dotted)
E= midpoint(segment(B,C))
draw(segment(A,E), dotted)
F= midpoint(segment(C,A))
draw(segment(B,F), dotted)

color(blue)
H = projection(C, line(A, B))
draw(segment(C, H), dashed)
I = projection(A, line(B,C))
draw(segment(A,I), dashed)
J = projection(B, line(C,A))
draw(segment(B,J), dashed)

color(red)
draw(circle(D,E,F))

color(black)
draw(D)
draw(E)
draw(F)

color(blue)
draw(H)
draw(I)
draw(J)