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Problem 538 from Connelly's corpus: Hb, Ma, N


Problem

Given a point Hb, a point Ma and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Ma and the point N, construct a line m(HbHc) (rule W02);

    % DET: points Ma and N are not the same

  2. Using the point Ma and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Ma and N are not the same

  3. Choose freely a point Hb on the circle k(N,Ma) (rule WOncircle)

  4. Using the circle k(N,Ma), the line m(HbHc), the point N and the point Ma, construct a point Ea (rule W05a);

    % NDG: line m(HbHc) and circle k(N,Ma) intersect

    % DET: points Ma and Ea must be different

  5. Using the point Hb and the point Ma, construct a circle k(Ma,B) (rule W06);

    % NDG: points Hb and Ma are not the same

  6. Using the circle k(N,Ma), the circle k(Ma,B), the point Hb, the point N and the point Ma, construct a point Hc (rule W08);

    % NDG: circles k(N,Ma) and k(Ma,B) intersect

    % DET: circles k(N,Ma) and k(Ma,B) are not the same points Hb and Hc must be different

  7. Choose freely a point A on the circle k(Ea,A) (rule WOncircle)

  8. Using the point A and the point Ea, construct a point H (rule W01);

  9. Using the point A and the point Hb, construct a line b (rule W02);

    % DET: points A and Hb are not the same

  10. Using the point Hc and the point H, construct a line hc (rule W02);

    % DET: points Hc and H are not the same

  11. Using the line b and the line hc, construct a point C (rule W03);

    % NDG: lines b and hc are not parallel

    % DET: lines b and hc are not the same

  12. Using the point Ma and the point C, construct a point B (rule W01);

animation
Construction in GCLC language

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