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Problem 514 from Wernick's corpus: Ha, Hc, Tc


Problem

Given a point Ha, a point Hc and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Ha and the point Hc, construct a line HcHa (rule W02);

    % DET: points Ha and Hc are not the same

  2. Using the point Hc and the point Tc, construct a line c (rule W02);

    % DET: points Hc and Tc are not the same

  3. Using the point Hc and the line c, construct a line hc (rule W10b);

  4. Using the line c, the line HcHa, the point Tc, the point Hc and the point Ha, construct a line HbHc (rule W18);

    % NDG: points Tc and Hc are not the same points Hc and Ha are not the same

    % DET: points Hc and Tc are not the same

  5. Using the point Tc, the point Hc and the point Ha, construct a circle circle[Tc,Ha,angle[s[c]][a]] (rule W20);

    % NDG: points Tc and Hc are not the same points Hc and Ha are not the same points Tc and Ha are not the same

  6. Using the circle circle[Tc,Ha,angle[s[c]][a]] and the line hc, construct a point Cca1 and a point C (rule W04);

    % NDG: line hc and circle circle[Tc,Ha,angle[s[c]][a]] intersect

  7. Using the point C and the point Ha, construct a line a (rule W02);

    % DET: points C and Ha are not the same

  8. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

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

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

    % NDG: points Hc and Ma are not the same

  11. Using the circle k(Ma,B), the line HbHc, the point Ma and the point Hc, construct a point Hb (rule W05);

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

    % DET: points Hc and Hb must be different

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

    % DET: points C and Hb are not the same

  13. Using the line c and the line b, construct a point A (rule W03);

    % NDG: lines c and b are not parallel

    % DET: lines c and b are not the same

animation
Construction in GCLC language

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