Using the point E_c and the point N, construct a line m(H_bH_a) (rule W02);

% DET: points E_c and N are not the same

Using the point E_c and the point N, construct a circle k(N,M_a) (rule W06);

% NDG: points E_c and N are not the same

Using the circle k(N,M_a), the line m(H_bH_a), the point N and the point E_c, construct a point M_c (rule W05a);

% NDG: line m(H_bH_a) and circle k(N,M_a) intersect

% DET: points E_c and M_c must be different

Using the point M_c and the point I, construct a line IM_c (rule W02);

% DET: points M_c and I are not the same

Using the point I and the point M_c, construct a circle k_over(I,M_c) (rule W09);

% NDG: points I and M_c are not the same

Using the point I, the circle k(N,M_a), the point N and the point E_c, construct a circle k(I,P_a) (rule W22);

% NDG: point I is inside the circle k(N,M_a) points I and N are not the same

Using the circle k(I,P_a) and the circle k_over(I,M_c), construct a point C_fi and a point P_c (rule W07);

% NDG: circles k(I,P_a) and k_over(I,M_c) intersect

% DET: circles k(I,P_a) and k_over(I,M_c) are not the same

Using the point P_c and the point M_c, construct a point P`_c (rule W01);

Using the circle k(I,P_a), the point M_c and the point I, construct a line x3 and a line c (rule W12);

% NDG: point M_c is outside the circle k(I,P_a)

Using the circle k(N,M_a), the line c, the point N and the point M_c, construct a point H_c (rule W05);

% NDG: line c and circle k(N,M_a) intersect

% DET: points M_c and H_c must be different

Using the point H_c and the point E_c, construct a line h_c (rule W02);

% DET: points H_c and E_c are not the same

Using the point M_c and the line c, construct a line m_c (rule W10b);

Using the point P`<sub>c</sub> and the line IM<sub>c</sub>, construct a line CP`_c (rule W16);

Using the line CP`_c and the line h_c, construct a point C (rule W03);

% NDG: lines CP`_c and h_c are not parallel

% DET: lines CP`_c and h_c are not the same

Using the point I and the point C, construct a line s_c (rule W02);

% DET: points I and C are not the same

Using the line m_c and the line s_c, construct a point N_c (rule W03);

% NDG: lines m_c and s_c are not parallel

% DET: lines m_c and s_c are not the same

Using the point I and the point N_c, construct a circle k(N_c,B) (rule W06);

% NDG: points I and N_c are not the same

Using the circle k(N_c,B) and the line c, construct a point B and a point A (rule W04);

% NDG: line c and circle k(N_c,B) intersect