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Problem 559 from Wernick's corpus: Ta, Tc, I


Problem

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

    % DET: points Ta 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 Tc, the point I and the point Ta, construct a circle circle[Ta,I,angle[a][s[b]]] (rule W20);

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

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

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

  5. Using the circle circle[Tc,Ta,angle[a][c]] and the circle circle[Ta,I,angle[a][s[b]]], construct a point Bc1 and a point B (rule W07);

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

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

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

    % DET: points B and Ta are not the same

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

    % DET: points Tc and B are not the same

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

    % NDG: lines sa and c are not parallel

    % DET: lines sa and c are not the same

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

    % NDG: lines sc and a are not parallel

    % DET: lines sc and a are not the same

 animation
Construction in GCLC language

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