Problem 516 from Wernick's corpus: H, Ha, Ta


Problem

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

Status

ArgoTriCS says that the problem is locus dependent.

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. Choose freely a point H on the line ha (rule WOnline2)

  4. Choose freely a point A on the line ha (rule WOnline1)

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

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

    % DET: points A and Ta are not the same

  7. Using the point H, the point A, the point Ta, the line sa and the line ha, construct a line AO (rule W17);

    % NDG: points A and Ta are not the same points H and A are not the same

    % DET: points A and Ta are not the same

  8. Using the point Ea and the line AO, construct a line m(HbHc) (rule W16);

  9. Using the line m(HbHc) and the line a, construct a point Ma (rule W03);

    % NDG: lines m(HbHc) and a are not parallel

    % DET: lines m(HbHc) and a are not the same

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

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

  12. 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

  13. 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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