Problem 179 from Wernick's corpus: B, Hb, Tb


Problem

Given a point B, a point Hb and a point Tb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


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

    % DET: points Hb and Tb are not the same

  2. Using the point Hb and the line b, construct a line hb (rule W10b);

  3. Choose freely a point B on the line hb (rule WOnline2)

  4. Using the point B and the point Tb, construct a line sb (rule W02);

    % DET: points B and Tb are not the same

  5. Using the point Hb, the point B, the point Tb, the line sb and the line hb, construct a line BO (rule W17);

    % NDG: points B and Tb are not the same points Hb and B are not the same

    % DET: points B and Tb are not the same

  6. Choose freely a point A on the line b (rule WOnline1)

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

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

    % DET: points A and B are not the same

  9. Using the point Mc and the line c, construct a line mc (rule W10b);

  10. Using the line mc and the line BO, construct a point O (rule W03);

    % NDG: lines mc and BO are not parallel

    % DET: lines mc and BO are not the same

  11. Using the point A and the point O, construct a circle k(O,C) (rule W06);

    % NDG: points A and O are not the same

  12. Using the circle k(O,C), the line b, the point O and the point A, construct a point C (rule W05);

    % NDG: line b and circle k(O,C) intersect

    % DET: points A and C must be different

animation
Construction in GCLC language

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