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Problem 334 from Connelly's corpus: Eb, H, Ha


Problem

Given a point Eb, a point H and a point Ha, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point H and the point Ha, construct a line ha (rule W02);

    % DET: points H and Ha are not the same

  2. Using the point Ha and the line ha, construct a line a (rule W10a);

  3. Using the point H, the line a and the point Ha, construct a line hH,1/2(a) (rule W15);

  4. Choose freely a point Eb on the line hH,1/2(a) (rule WOnline4)

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

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

    % NDG: points H and Eb are not the same

  7. Choose freely a point A on the line ha (rule WOnline1)

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

    % DET: points A and B are not the same

  9. 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

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

    % DET: points Hc and H are not the same

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

    % NDG: lines a and hc are not parallel

    % DET: lines a and hc are not the same

animation
Construction in GCLC language

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