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Problem 192 from Wernick's corpus: B, Ta, Tc


Problem

Given a point B, a point Ta 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 B and the point Ta, construct a line a (rule W02);

    % DET: points B and Ta are not the same

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

    % DET: points B and Tc are not the same

  3. Using the line c, the point Ta, the point B, the point Tc and the line a, construct a line sb (rule W17);

    % NDG: points B and Tc are not the same points Ta and B are not the same

    % DET: points B and Ta are not the same

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

    % NDG: points Ta and B are not the same points B and Tc are not the same points Tc and Ta are not the same

  5. Using the circle circle[Tc,Ta,angle[s[c]][s[a]]] and the line sb, construct a point Bsa and a point I (rule W04);

    % NDG: line sb and circle circle[Tc,Ta,angle[s[c]][s[a]]] intersect

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

    % DET: points I and Ta 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 a and the line sc, construct a point C (rule W03);

    % NDG: lines a and sc are not parallel

    % DET: lines a and sc are not the same

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

    % NDG: lines c and sa are not parallel

    % DET: lines c and sa are not the same

 animation
Construction in GCLC language

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