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Problem 230 from Connelly's corpus: Ea, H, Hb


Problem

Given a point Ea, 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 Ea on the line hH,1/2(b) (rule WOnline4)

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

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

    % NDG: points H and Ea are not the same

  7. Choose freely a point B on the line hb (rule WOnline1)

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

    % DET: points B and A are not the same

  9. Using the circle k(Ea,A), the line c, the point Ea and the point A, construct a point Hc (rule W05);

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

    % DET: points A 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 b and the line hc, construct a point C (rule W03);

    % NDG: lines b and hc are not parallel

    % DET: lines b and hc are not the same

animation
Construction in GCLC language

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