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Problem 427 from Connelly's corpus: Ec, H, Hc


Problem

Given a point Ec, 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. Choose freely a point Ec on the line hc (rule WOnline1)

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

  4. 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

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

  6. Choose freely a point A on the line c (rule WOnline2)

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

    % DET: points A and H are not the same

  8. 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

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

    % DET: points C and Ha are not the same

  10. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

animation
Construction in GCLC language

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