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Problem 188 from Wernick's corpus: B, H, Tb


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point B and the point H, construct a point Eb (rule W01);

  2. Using the point B and the point H, construct a line hb (rule W02);

    % DET: points B and H are not the same

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

    % DET: points B and Tb are not the same

  4. Using the point Tb and the line hb, construct a line b (rule W10a);

  5. Using the point H, 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 H and B are not the same

    % DET: points B and Tb are not the same

  6. Using the point Eb and the line BO, construct a line m(HaHc) (rule W16);

  7. Using the line m(HaHc) and the line b, construct a point Mb (rule W03);

    % NDG: lines m(HaHc) and b are not parallel

    % DET: lines m(HaHc) and b are not the same

  8. Using the point Mb and the point B, construct a point G (rule W01);

  9. Using the point H and the point G, construct a point O (rule W01);

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

    % NDG: points B and O are not the same

  11. Using the circle k(O,C) and the line b, construct a point C and a point A (rule W04);

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

animation
Construction in GCLC language

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