Problem 414 from Wernick's corpus: Ha, Mb, Hc


Problem

Given a point Ha, a point Mb and a point Hc, 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 Mb, construct a circle k(Mb,C) (rule W06);

    % NDG: points Hc and Mb are not the same

  2. Choose freely a point Ha on the circle k(Mb,C) (rule WOncircle)

  3. Using the point Ha and the point Mb, construct a line m(HaMb) (rule W14);

    % DET: points Ha and Mb are not the same

  4. Using the point Ha and the point Hc, construct a line m(HaHc) (rule W14);

    % DET: points Ha and Hc are not the same

  5. Using the line m(HaHc) and the line m(HaMb), construct a point N (rule W03);

    % NDG: lines m(HaHc) and m(HaMb) are not parallel

    % DET: lines m(HaHc) and m(HaMb) are not the same

  6. Choose freely a point A on the circle k(Mb,C) (rule WOncircle)

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

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

    % DET: points A and Ha are not the same

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

    % DET: points Hc and C are not the same

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

    % NDG: lines ha and hc are not parallel

    % DET: lines ha and hc are not the same

  11. Using the point N and the point H, construct a point G (rule W01);

  12. Using the point Mb and the point G, construct a point B (rule W01);

animation
Construction in GCLC language

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