Back to the list of problems

Problem 371 from Connelly's corpus: Eb, Hc, N


Problem

Given a point Eb, a point Hc and a point N, 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 N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Hc and N are not the same

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

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

    % DET: points Eb and N are not the same

  4. Using the circle k(N,Ma), the line m(HaHc), the point N and the point Eb, construct a point Mb (rule W05a);

    % NDG: line m(HaHc) and circle k(N,Ma) intersect

    % DET: points Eb and Mb must be different

  5. 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

  6. 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

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

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

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

    % DET: points A and Hc are not the same

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

    % DET: points Ha and C are not the same

  11. 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