Problem 250 from Wernick's corpus: C, Ha, Ta


Problem

Given a point C, 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. Choose freely a point C on the line a (rule WOnline1)

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

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

  5. Using the point A and the point C, construct a line b (rule W02);

    % DET: points A and C are not the same

  6. Using the point Ta and the line b, construct a circle k(Ta,foot[Ta,c]) (rule W11);

    % NDG: point Ta is not incident to the line b

  7. Using the circle k(Ta,foot[Ta,c]), the point A, the point Ta and the line b, construct a line c (rule W13);

    % NDG: point A is outside the circle k(Ta,foot[Ta,c])

  8. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

animation
Construction in GCLC language

Back to the list of problems