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Problem 480 from Wernick's corpus: G, Ha, Ta


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Ha and the point Ta, construct a line a (rule W02);

    % DET: points Ha and Ta are not the same

  2. Using the point Ha and the line a, construct a line ha (rule W10b);

  3. Using the point G, the line a and the point Ha, construct a line hG,-2/1(a) (rule W15);

  4. Using the line hG,-2/1(a) and the line ha, construct a point A (rule W03);

    % NDG: lines hG,-2/1(a) and ha are not parallel

    % DET: lines hG,-2/1(a) and ha are not the same

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

  6. Using the point Ta and the point A, construct a line sa (rule W02);

    % DET: points Ta and A are not the same

  7. Using the point Ma and the line a, construct a line ma (rule W10b);

  8. Using the line ma and the line sa, construct a point Na (rule W03);

    % NDG: lines ma and sa are not parallel

    % DET: lines ma and sa are not the same

  9. Using the point A and the point Na, construct a line m(ANa) (rule W14);

    % DET: points A and Na are not the same

  10. Using the line m(ANa) and the line ma, construct a point O (rule W03);

    % NDG: lines m(ANa) and ma are not parallel

    % DET: lines m(ANa) and ma 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) 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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