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Problem 426 from Connelly's corpus: Ec, H, Hb


Problem

Given a point Ec, a point H 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 H and the point Hb, construct a line hb (rule W02);

    % DET: points H and Hb are not the same

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

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

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

  5. Using the point Ec and the point H, construct a point C (rule W01);

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

    % NDG: points H and Ec are not the same

  7. Choose freely a point A on the line b (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(Ec,C), the line ha, the point Ec and the point H, construct a point Ha (rule W05);

    % NDG: line ha and circle k(Ec,C) intersect

    % DET: points H and Ha must be different

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

    % DET: points C and Ha are not the same

  11. Using the line hb and the line a, construct a point B (rule W03);

    % NDG: lines hb and a are not parallel

    % DET: lines hb and a are not the same

animation
Construction in GCLC language

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