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  • Feuerbach's Circle

    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