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Problem 386 from Connelly's corpus: Eb, Ma, N


Problem

Given a point Eb, a point Ma 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 Ma and the point N, construct a line m(HbHc) (rule W02);

    % DET: points Ma and N are not the same

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

    % NDG: points Ma and N are not the same

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

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

    % DET: points Eb and N are not the same

  5. Using the circle k(N,Ma), the line m(HbHc), the point N and the point Ma, construct a point Ea (rule W05a);

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

    % DET: points Ma and Ea must be different

  6. 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

  7. Choose freely a point A (rule free)

  8. Using the point A and the point Ea, construct a point H (rule W01);

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

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

animation
Construction in GCLC language

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