Problem 274 from Wernick's corpus: C, Tc, I


Problem

Given a point C, a point Tc 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 Tc and the point I, construct a line sc (rule W02);

    % DET: points Tc and I are not the same

  2. Choose freely a point C on the line sc (rule WOnline1)

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

    % DET: points C and I are not the same

  4. Choose freely a point A (rule free)

  5. Using the point A and the point C, construct a point Mb (rule W01);

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

    % DET: points A and C are not the same

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

    % DET: points A and Tc are not the same

  8. Using the point Mb and the line b, construct a line mb (rule W10b);

  9. Using the line mb and the line m(CI), construct a point Nb (rule W03);

    % NDG: lines mb and m(CI) are not parallel

    % DET: lines mb and m(CI) are not the same

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

    % DET: points Nb and I are not the same

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

    % NDG: lines c and sb are not parallel

    % DET: lines c and sb are not the same

animation
Construction in GCLC language

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