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Problem 29 from Connelly's corpus: A, Eb, Hb


Problem

Given a point A, a point Eb and a point Hb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Eb and the point Hb, construct a line hb (rule W02);

    % DET: points Eb and Hb are not the same

  2. Using the point Hb and the line hb, construct a line b (rule W10a);

  3. Choose freely a point A on the line b (rule WOnline2)

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

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

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

    % DET: points B and A are not the same

  7. Using the point B and the point Eb, construct a circle k(Eb,B) (rule W06);

    % NDG: points B and Eb are not the same

  8. Using the circle k(Eb,B), the line c, the point Eb and the point B, construct a point Hc (rule W05);

    % NDG: line c and circle k(Eb,B) intersect

    % DET: points B and Hc must be different

  9. Using the point H and the point Hc, construct a line hc (rule W02);

    % DET: points H and Hc are not the same

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

    % NDG: lines b and hc are not parallel

    % DET: lines b and hc are not the same

animation
Construction in GCLC language

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