Using the point E_a and the point M_a, construct a line m(H_bH_c) (rule W02);

% DET: points E_a and M_a are not the same

Using the point I and the point M_a, construct a line IM_a (rule W02);

% DET: points I and M_a are not the same

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

% NDG: points I and M_a are not the same

Using the point E_a and the point M_a, construct a line m(E_aM_a) (rule W14);

% DET: points E_a and M_a are not the same

Using the line m(E_aM_a) and the line m(H_bH_c), construct a point N (rule W03);

% NDG: lines m(E_aM_a) and m(H_bH_c) are not parallel

% DET: lines m(E_aM_a) and m(H_bH_c) are not the same

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

% NDG: points E_a and N are not the same

Using the point I, the circle k(N,M_a), the point N and the point E_a, 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_a), construct a point P_a and a point A_fi (rule W07);

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

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

Using the point P_a and the point M_a, construct a point P`_a (rule W01);

Using the circle k(I,P_a), the point M_a and the point I, construct a line x1 and a line a (rule W12);

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

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

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

% DET: points M_a and H_a must be different

Using the point H_a and the point E_a, construct a line h_a (rule W02);

% DET: points H_a and E_a are not the same

Using the point M_a and the line a, construct a line m_a (rule W10b);

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

Using the line AP`_a and the line h_a, construct a point A (rule W03);

% NDG: lines AP`_a and h_a are not parallel

% DET: lines AP`_a and h_a are not the same

Using the point I and the point A, construct a line s_a (rule W02);

% DET: points I and A are not the same

Using the line m_a and the line s_a, construct a point N_a (rule W03);

% NDG: lines m_a and s_a are not parallel

% DET: lines m_a and s_a are not the same

Using the point I and the point N_a, construct a circle k(N_a,C) (rule W06);

% NDG: points I and N_a are not the same

Using the circle k(N_a,C) and the line a, construct a point C and a point B (rule W04);

% NDG: line a and circle k(N_a,C) intersect