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Problem 558 from Wernick's corpus: Ta, Tb, I


Problem

Given a point Ta, a point Tb 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 Ta and the point I, construct a line sa (rule W02);

    % DET: points Ta and I are not the same

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

    % DET: points Tb and I are not the same

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

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

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

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

  5. Using the circle circle[Tb,I,angle[b][s[c]]] and the circle circle[Ta,Tb,angle[b][a]], construct a point Cc1 and a point C (rule W07);

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

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

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

    % DET: points C and Ta are not the same

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

    % DET: points Tb and C are not the same

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

    % NDG: lines sa and b are not parallel

    % DET: lines sa and b are not the same

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

    % NDG: lines sb and a are not parallel

    % DET: lines sb and a are not the same

animation
Construction in GCLC language

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