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Problem 269 from Wernick's corpus: C, Ta, Tb


Problem

Given a point C, a point Ta and a point Tb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point C and the point Ta, construct a line a (rule W02);

    % DET: points C and Ta are not the same

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

    % DET: points C and Tb are not the same

  3. Using the line a, the point Tb, the point C, the point Ta and the line b, construct a line sc (rule W17);

    % NDG: points C and Ta are not the same points Tb and C are not the same

    % DET: points C and Tb are not the same

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

    % NDG: points Tb and C are not the same points C and Ta are not the same points Ta and Tb are not the same

  5. Using the circle circle[Ta,Tb,angle[s[a]][s[b]]] and the line sc, construct a point Csa and a point I (rule W04);

    % NDG: line sc and circle circle[Ta,Tb,angle[s[a]][s[b]]] 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 Tb and the point I, construct a line sb (rule W02);

    % DET: points Tb and I are not the same

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

    % NDG: lines a and sb are not parallel

    % DET: lines a and sb are not the same

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

    % NDG: lines b and sa are not parallel

    % DET: lines b and sa are not the same

animation
Construction in GCLC language

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