Problem 260 from Wernick's corpus: C, Hc, H


Problem

Given a point C, 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. Choose freely a point C on the line hc (rule WOnline1)

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

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

  5. Using the point A and the point C, construct a point Mb (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 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 ha, the point Mb and the point A, construct a point Ha (rule W05);

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

    % DET: points A and Ha must be different

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

    % DET: points Ha and C are not the same

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

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

animation
Construction in GCLC language

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