Problem 81 from Wernick's corpus: A, Ha, Ta


Problem

Given a point A, 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 A on the line ha (rule WOnline2)

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

    % DET: points A and Ta are not the same

  5. Using the point Ha, 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 Ha and A are not the same

    % DET: points A and Ta are not the same

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

  7. Using the point B and the point A, construct a point Mc (rule W01);

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

    % DET: points B and A are not the same

  9. Using the point Mc and the line c, construct a line mc (rule W10b);

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

    % NDG: lines mc and AO are not parallel

    % DET: lines mc and AO are not the same

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

    % NDG: points B and O are not the same

  12. Using the circle k(O,C), the line a, the point O and the point B, construct a point C (rule W05);

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

    % DET: points B and C must be different

animation
Construction in GCLC language

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