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Problem 398 from Connelly's corpus: Eb, Mc, O


Problem

Given a point Eb, a point Mc and a point O, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Eb and the point Mc, construct a line m(BHa) (rule W02);

    % DET: points Eb and Mc are not the same

  2. Using the point Mc and the point O, construct a line mc (rule W02);

    % DET: points Mc and O are not the same

  3. Using the point Mc and the line mc, construct a line c (rule W10a);

  4. Using the point Eb and the line mc, construct a line m(BHc) (rule W16);

  5. Using the point O and the line m(BHa), construct a line ma (rule W16);

  6. Using the line ma and the line m(BHc), construct a point Ma (rule W03);

    % NDG: lines ma and m(BHc) are not parallel

    % DET: lines ma and m(BHc) are not the same

  7. Using the point Ma and the line ma, construct a line a (rule W10a);

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

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

  9. Using the point B and the point Eb, construct a point H (rule W01);

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

  11. Using the point O and the point H, construct a point G (rule W01);

  12. Using the point Mc and the point G, construct a point C (rule W01);

animation
Construction in GCLC language

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