Feuerbach's Circle

A B C triangle

A' = projection(A, line(B, C))
B' = projection(B, line(C, A))
C' = projection(C, line(A, B))

A_0 = midpoint(B.C)
B_0 = midpoint(C.A)
C_0 = midpoint(A.B)

draw
  (A.B.C)
  circle(A', B', C')
  A'; B'; C'
  A_0 ; B_0 ; C_0
end
draw dashed
  A.A' ; B.B' ; C.C'
end

label
  A -135° ; B -45° ; C 90°
  A' 45° ; B' 135° ; C' -90°
  A_0 30° ; B_0 150° ; C_0 -90°
end