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Problem 58 from Connelly's corpus: A, Hc, N


Problem

Given a point A, a point Hc 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 Hc, construct a line c (rule W02);

    % DET: points A and Hc are not the same

  2. 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

  3. Using the circle k(N,Ma), the line c, the point N and the point Hc, construct a point Mc (rule W05);

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

    % DET: points Hc and Mc must be different

  4. Using the point Mc and the point A, construct a point B (rule W01);

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

    % DET: points N and Mc are not the same

  6. Using the circle k(N,Ma), the line m(HaHb), the point N and the point Mc, construct a point Ec (rule W05a);

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

    % DET: points Mc and Ec must be different

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

    % DET: points Ec and Hc are not the same

  8. Using the point A and the point Mc, construct a circle k(Mc,A) (rule W06);

    % NDG: points A and Mc are not the same

  9. Using the circle k(N,Ma) and the circle k(Mc,A), construct a point Ha and a point Hb (rule W07);

    % NDG: circles k(N,Ma) and k(Mc,A) intersect

    % DET: circles k(N,Ma) and k(Mc,A) 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 hc and the line ha, construct a point H (rule W03);

    % NDG: lines hc and ha are not parallel

    % DET: lines hc 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 Mc and the point G, construct a point C (rule W01);

animation
Construction in GCLC language

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