Problem 182 from Wernick's corpus: B, Hc, H


Problem

Given a point B, a point Hc and a point H, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Hc and the point H, construct a line hc (rule W02);

    % DET: points Hc and H are not the same

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

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

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

    % DET: points B and H are not the same

  5. Choose freely a point A on the line c (rule WOnline1)

  6. Using the point A and the point B, construct a point Mc (rule W01);

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

    % NDG: points A and Mc are not the same

  8. Using the circle k(Mc,A), the line hb, the point Mc and the point B, construct a point Hb (rule W05);

    % NDG: line hb and circle k(Mc,A) intersect

    % DET: points B and Hb must be different

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

    % DET: points Hb and A are not the same

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

    % NDG: lines hc and b are not parallel

    % DET: lines hc and b are not the same

animation
Construction in GCLC language

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