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Problem 507 from Wernick's corpus: Ha, Hb, Ta


Problem

Given a point Ha, a point Hb 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 Hb, construct a line HaHb (rule W02);

    % DET: points Ha and Hb 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 line a, the line HaHb, the point Ta, the point Ha and the point Hb, construct a line HcHa (rule W18);

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

    % DET: points Ha and Ta are not the same

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

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

  6. Using the circle circle[Ta,Hb,angle[s[a]][b]] and the line ha, construct a point Aca1 and a point A (rule W04);

    % NDG: line ha and circle circle[Ta,Hb,angle[s[a]][b]] intersect

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

    % DET: points A and Hb are not the same

  8. 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

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

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

    % NDG: points Ha and Mb are not the same

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

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

    % DET: points Ha and Hc must be different

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

    % DET: points A and Hc are not the same

  13. 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

animation
Construction in GCLC language

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