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Problem 512 from Wernick's corpus: Ha, Hc, Ta


Problem

Given a point Ha, a point Hc and a point Ta, 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 Ha and the point Ta, construct a line a (rule W02);

    % DET: points Ha and Ta are not the same

  3. Using the point Ha and the line a, construct a line ha (rule W10b);

  4. Using the point Hc, the point Ha, the point Ta, the line a and the line HcHa, construct a line HaHb (rule W17);

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

    % DET: points Ha and Ta are not the same

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

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

  6. Using the circle circle[Ta,Hc,angle[c][s[a]]] and the line ha, construct a point Aca2 and a point A (rule W04);

    % NDG: line ha and circle circle[Ta,Hc,angle[c][s[a]]] intersect

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

    % DET: points A and Hc are not the same

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

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

  9. Using the point B and the point A, construct a point Mc (rule W01);

  10. Using the point Ha and the point Mc, construct a circle k(Mc,A) (rule W06);

    % NDG: points Ha and Mc are not the same

  11. Using the circle k(Mc,A), the line HaHb, the point Mc and the point Ha, construct a point Hb (rule W05);

    % NDG: line HaHb and circle k(Mc,A) intersect

    % DET: points Ha and Hb must be different

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

    % DET: points A and Hb are not the same

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

    % NDG: lines a and b are not parallel

    % DET: lines a and b are not the same

animation
Construction in GCLC language

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