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Problem 560 from Wernick's corpus: Tb, Tc, I


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Tb and I are not the same

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

    % DET: points Tc and I are not the same

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

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

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

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

  5. Using the circle circle[Tc,I,angle[c][s[a]]] and the circle circle[Tb,Tc,angle[c][b]], construct a point Ac2 and a point A (rule W07);

    % NDG: circles circle[Tc,I,angle[c][s[a]]] and circle[Tb,Tc,angle[c][b]] intersect

    % DET: circles circle[Tc,I,angle[c][s[a]]] and circle[Tb,Tc,angle[c][b]] are not the same

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

    % DET: points A and Tb are not the same

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

    % DET: points Tc and A are not the same

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

    % NDG: lines sb and c are not parallel

    % DET: lines sb and c are not the same

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

    % NDG: lines sc and b are not parallel

    % DET: lines sc and b are not the same

animation
Construction in GCLC language

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