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Problem 267 from Wernick's corpus: C, H, Tc


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

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

    % DET: points C and H are not the same

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

    % DET: points C and Tc are not the same

  4. Using the point Tc and the line hc, construct a line c (rule W10a);

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

    % DET: points C and Tc are not the same

  6. Using the point Ec and the line CO, construct a line m(HbHa) (rule W16);

  7. Using the line m(HbHa) and the line c, construct a point Mc (rule W03);

    % NDG: lines m(HbHa) and c are not parallel

    % DET: lines m(HbHa) and c are not the same

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

    % NDG: points C and O are not the same

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

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

animation
Construction in GCLC language

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