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Problem 305 from Wernick's corpus: O, G, Ha


Problem

Given a point O, a point G and a point Ha, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

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

    % DET: points Ha and H are not the same

  3. Using the point Ha and the line ha, construct a line a (rule W10a);

  4. Using the point O and the line a, construct a line ma (rule W10b);

  5. Using the line ma and the line a, construct a point Ma (rule W03);

    % NDG: lines ma and a are not parallel

    % DET: lines ma and a are not the same

  6. Using the point Ma and the point G, construct a point A (rule W01);

  7. 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

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

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

animation
Construction in GCLC language

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