Problem 177 from Wernick's corpus: B, Hb, H


Problem

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

    % DET: points Hb and H are not the same

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

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

  4. Choose freely a point A on the line b (rule WOnline2)

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

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

    % DET: points A and H are not the same

  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 ha, the point Mc and the point A, construct a point Ha (rule W05);

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

    % DET: points A and Ha must be different

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

    % DET: points Ha and B are not the same

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

    % NDG: lines b and a are not parallel

    % DET: lines b and a are not the same

animation
Construction in GCLC language

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