Problem 249 from Wernick's corpus: C, Ha, H


Problem

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

    % DET: points Ha and H 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. Using the point C and the point H, construct a line hc (rule W02);

    % DET: points C and H are not the same

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

  6. Using the point A and the point C, construct a point Mb (rule W01);

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

    % NDG: points A and Mb are not the same

  8. Using the circle k(Mb,C), the line hc, the point Mb and the point C, construct a point Hc (rule W05);

    % NDG: line hc and circle k(Mb,C) intersect

    % DET: points C and Hc must be different

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

    % DET: points Hc and A are not the same

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

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

animation
Construction in GCLC language

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