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Problem 133 from Connelly's corpus: C, Ea, Ha


Problem

Given a point C, a point Ea 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 Ea and the point Ha, construct a line ha (rule W02);

    % DET: points Ea and Ha are not the same

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

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

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

  5. Using the point A and the point Ea, construct a point H (rule W01);

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

    % DET: points A and C are not the same

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

    % NDG: points A and Ea are not the same

  8. Using the circle k(Ea,A), the line b, the point Ea and the point A, construct a point Hb (rule W05);

    % NDG: line b and circle k(Ea,A) intersect

    % DET: points A and Hb must be different

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

    % DET: points H and Hb are not the same

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

    % NDG: lines a and hb are not parallel

    % DET: lines a and hb are not the same

animation
Construction in GCLC language

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