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Problem 385 from Connelly's corpus: Eb, Ma, Mc


Problem

Given a point Eb, a point Ma and a point Mc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Eb and the point Ma, construct a line m(EbMa) (rule W14);

    % DET: points Eb and Ma are not the same

  2. Using the point Eb and the point Mc, construct a line m(EbMc) (rule W14);

    % DET: points Eb and Mc are not the same

  3. Using the line m(EbMc) and the line m(EbMa), construct a point N (rule W03);

    % NDG: lines m(EbMc) and m(EbMa) are not parallel

    % DET: lines m(EbMc) and m(EbMa) are not the same

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

    % DET: points Ma and N are not the same

  5. 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

  6. 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

  7. Using the point Mc and the point Ea, construct a line m(AHb) (rule W02);

    % DET: points Mc and Ea are not the same

  8. Using the point Eb and the line m(AHb), construct a line hb (rule W16);

  9. Using the circle k(N,Ma), the line hb, the point N and the point Eb, construct a point Hb (rule W05);

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

    % DET: points Eb and Hb must be different

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

    % NDG: points Hb and Ma are not the same

  11. Using the circle k(Ma,B), the line hb, the point Ma and the point Hb, construct a point B (rule W05);

    % NDG: line hb and circle k(Ma,B) intersect

    % DET: points Hb and B must be different

  12. Using the point Ma and the point B, construct a point C (rule W01);

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

animation
Construction in GCLC language

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