Problem 195 from Wernick's corpus: B, Tb, I


Problem

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

Status

ArgoTriCS says that the problem is locus dependent.

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. Choose freely a point B on the line sb (rule WOnline1)

  3. Using the point B and the point I, construct a line m(BI) (rule W14);

    % DET: points B and I are not the same

  4. Choose freely a point A (rule free)

  5. Using the point A and the point B, construct a point Mc (rule W01);

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

    % DET: points A and B are not the same

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

    % DET: points A and Tb are not the same

  8. Using the point Mc and the line c, construct a line mc (rule W10b);

  9. Using the line mc and the line m(BI), construct a point Nc (rule W03);

    % NDG: lines mc and m(BI) are not parallel

    % DET: lines mc and m(BI) are not the same

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

    % DET: points Nc and I are not the same

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

    % NDG: lines b and sc are not parallel

    % DET: lines b and sc are not the same

animation
Construction in GCLC language

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