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Problem 103 from Wernick's corpus: A, Tb, Tc


Problem

Given a point A, a point Tb and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points A and Tb are not the same

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

    % DET: points A and Tc are not the same

  3. Using the line b, the point Tc, the point A, the point Tb and the line c, construct a line sa (rule W17);

    % NDG: points A and Tb are not the same points Tc and A are not the same

    % DET: points A and Tc are not the same

  4. Using the point Tc, the point A and the point Tb, construct a circle circle[Tb,Tc,angle[s[b]][s[c]]] (rule W20);

    % NDG: points Tc and A are not the same points A and Tb are not the same points Tb and Tc are not the same

  5. Using the circle circle[Tb,Tc,angle[s[b]][s[c]]] and the line sa, construct a point Asa and a point I (rule W04);

    % NDG: line sa and circle circle[Tb,Tc,angle[s[b]][s[c]]] intersect

  6. Using the point I and the point Tb, construct a line sb (rule W02);

    % DET: points I and Tb are not the same

  7. Using the point Tc and the point I, construct a line sc (rule W02);

    % DET: points Tc and I are not the same

  8. Using the line b and the line sc, construct a point C (rule W03);

    % NDG: lines b and sc are not parallel

    % DET: lines b and sc are not the same

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

    % NDG: lines c and sb are not parallel

    % DET: lines c and sb are not the same

animation
Construction in GCLC language

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