Back to the list of problems

Problem 369 from Connelly's corpus: Hc, Eb, Mb


Problem

Given a point Hc, 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 Hc on the circle k(N,Ma) (rule WOncircle)

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

    % NDG: points Hc and Eb are not the same

  7. Using the circle k(N,Ma), the circle k(Eb,B), the point Hc, the point N and the point Eb, construct a point Ha (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 Hc and Ha 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 Hc, construct a line c (rule W02);

    % DET: points A and Hc are not the same

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

    % DET: points Ha and C are not the same

  12. 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

Back to the list of problems