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Problem 350 from Connelly's corpus: Ha, Eb, Mb


Problem

Given a point Ha, a point Eb and a point Mb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Eb and the point Mb, construct a line m(HaHc) (rule W02);

    % DET: points Eb and Mb are not the same

  2. Using the point Eb and the point Mb, construct a line m(EbMb) (rule W14);

    % DET: points Eb and Mb are not the same

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

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

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

  4. Using the point Eb and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Eb and N are not the same

  5. Choose freely a point Ha on the circle k(N,Ma) (rule WOncircle)

  6. Using the point Ha and the point Eb, construct a circle k(Eb,B) (rule W06);

    % NDG: points Ha and Eb are not the same

  7. Using the circle k(N,Ma), the circle k(Eb,B), the point Ha, the point N and the point Eb, construct a point Hc (rule W08);

    % NDG: circles k(N,Ma) and k(Eb,B) intersect

    % DET: circles k(N,Ma) and k(Eb,B) are not the same points Ha and Hc must be different

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

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

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

    % DET: points A and Ha are not the same

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

    % DET: points Hc and C are not the same

  12. 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

  13. Using the point Eb and the point H, construct a point B (rule W01);

animation
Construction in GCLC language

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