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Problem 57 from Connelly's corpus: A, Hb, N


Problem

Given a point A, a point Hb and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point A and the point Hb, construct a line b (rule W02);

    % DET: points A and Hb are not the same

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

    % NDG: points Hb and N are not the same

  3. Using the circle k(N,Ma), the line b, the point N and the point Hb, construct a point Mb (rule W05);

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

    % DET: points Hb and Mb must be different

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

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

    % DET: points N and Mb are not the same

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

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

    % DET: points Mb and Eb must be different

  7. Using the point Eb and the point Hb, construct a line hb (rule W02);

    % DET: points Eb and Hb are not the same

  8. 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

  9. Using the circle k(N,Ma) and the circle k(Mb,C), construct a point Ha and a point Hc (rule W07);

    % NDG: circles k(N,Ma) and k(Mb,C) intersect

    % DET: circles k(N,Ma) and k(Mb,C) are not the same

  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 line hb and the line ha, construct a point H (rule W03);

    % NDG: lines hb and ha are not parallel

    % DET: lines hb and ha are not the same

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

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

animation
Construction in GCLC language

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