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Problem 336 from Connelly's corpus: Eb, H, Hc


Problem

Given a point Eb, a point H and a point Hc, 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 Hc, construct a line hc (rule W02);

    % DET: points H and Hc are not the same

  2. Using the point Hc and the line hc, construct a line c (rule W10a);

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

  4. Choose freely a point Eb on the line hH,1/2(c) (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 c (rule WOnline1)

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

    % DET: points A and H are not the same

  9. Using the circle k(Eb,B), the line ha, the point Eb and the point H, construct a point Ha (rule W05);

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

    % DET: points H and Ha must be different

  10. Using the point B and the point Ha, construct a line a (rule W02);

    % DET: points B and Ha are not the same

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

    % NDG: lines hc and a are not parallel

    % DET: lines hc and a are not the same

animation
Construction in GCLC language

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