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Problem 344 from Connelly's corpus: Eb, H, Tb


Problem

Given a point Eb, 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 Eb and the point H, construct a point B (rule W01);

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

    % DET: points Eb and H are not the same

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

    % DET: points Tb and B are not the same

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

  5. Using the line b and the line hb, construct a point Hb (rule W03);

    % NDG: lines b and hb are not parallel

    % DET: lines b and hb are not the same

  6. Using the point H and the point Hb, construct a line m(HHb) (rule W14);

    % DET: points H and Hb are not the same

  7. Using the point Eb, 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 Eb and B are not the same

    % DET: points B and Tb are not the same

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

  9. 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

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

  11. Using the point H and the point G, construct a point N (rule W01);

  12. Using the point Eb and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Eb and N are not the same

  13. Using the circle k(N,Ma) and the line m(HHb), construct a point Ea and a point Ec (rule W04);

    % NDG: line m(HHb) and circle k(N,Ma) intersect

  14. Using the point Ea and the point H, construct a point A (rule W01);

  15. Using the point H and the point Ec, construct a point C (rule W01);

animation
Construction in GCLC language

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