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Problem 288 from Connelly's corpus: Ea, Mb, O


Problem

Given a point Ea, a point Mb 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 Ea and the point Mb, construct a line m(AHc) (rule W02);

    % DET: points Ea and Mb are not the same

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

    % DET: points Mb and O are not the same

  3. Using the point Mb and the line mb, construct a line b (rule W10a);

  4. Using the point Ea and the line mb, construct a line m(AHb) (rule W16);

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

  6. Using the line mc and the line m(AHb), construct a point Mc (rule W03);

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

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

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

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

    % NDG: lines c and b are not parallel

    % DET: lines c and b are not the same

  9. Using the point A and the point Ea, construct a point H (rule W01);

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

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

  12. Using the point Mb and the point G, construct a point B (rule W01);

animation
Construction in GCLC language

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