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Problem 529 from Wernick's corpus: Hb, Hc, Tc


Problem

Given a point Hb, 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 Hb and the point Hc, construct a line HbHc (rule W02);

    % DET: points Hb 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 point Hb, the point Hc, the point Tc, the line c and the line HbHc, construct a line HcHa (rule W17);

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

    % DET: points Hc and Tc are not the same

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

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

  6. Using the circle circle[Tc,Hb,angle[b][s[c]]] and the line hc, construct a point Cca2 and a point C (rule W04);

    % NDG: line hc and circle circle[Tc,Hb,angle[b][s[c]]] intersect

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

    % DET: points C and Hb are not the same

  8. 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

  9. Using the point A and the point C, construct a point Mb (rule W01);

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

    % NDG: points Hc and Mb are not the same

  11. Using the circle k(Mb,C), the line HcHa, the point Mb and the point Hc, construct a point Ha (rule W05);

    % NDG: line HcHa and circle k(Mb,C) intersect

    % DET: points Hc and Ha must be different

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

    % DET: points C and Ha are not the same

  13. 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

animation
Construction in GCLC language

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