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Problem 313 from Connelly's corpus: Eb, Ec, Ma


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Ec and the point Ma, construct a line m(CHb) (rule W02);

    % DET: points Ec and Ma are not the same

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

    % DET: points Eb and Ec are not the same

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

    % DET: points Eb and Ma are not the same

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

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

    % DET: lines m(EbMa) and m(EbEc) 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 point Eb and the line m(CHb), construct a line hb (rule W16);

  7. 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

  8. Using the point Hb and the point Ec, construct a circle k(Ec,C) (rule W06);

    % NDG: points Hb and Ec are not the same

  9. Using the circle k(Ec,C), the line hb, the point Ec and the point Hb, construct a point H (rule W05);

    % NDG: line hb and circle k(Ec,C) intersect

    % DET: points Hb and H must be different

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

  11. Using the point Ec and the point H, construct a point C (rule W01);

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

  13. Using the point Ma and the point G, construct a point A (rule W01);

animation
Construction in GCLC language

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