Problem 263 from Wernick's corpus: C, Hc, Tc


Problem

Given a point C, a point Hc and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


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

    % DET: points Hc and Tc are not the same

  2. Using the point Hc and the line c, construct a line hc (rule W10b);

  3. Choose freely a point C on the line hc (rule WOnline2)

  4. Using the point C and the point Tc, construct a line sc (rule W02);

    % DET: points C and Tc are not the same

  5. Using the point Hc, the point C, the point Tc, the line sc and the line hc, construct a line CO (rule W17);

    % NDG: points C and Tc are not the same points Hc and C are not the same

    % DET: points C and Tc are not the same

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

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

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

    % DET: points A and C are not the same

  9. Using the point Mb and the line b, construct a line mb (rule W10b);

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

    % NDG: lines mb and CO are not parallel

    % DET: lines mb and CO 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 c, the point O and the point A, construct a point B (rule W05);

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

    % DET: points A and B must be different

animation
Construction in GCLC language

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