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Problem 209 from Connelly's corpus: Ea, Ec, Mb


Problem

Given a point Ea, a point Ec and a point Mb, 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 Mb, construct a line m(CHa) (rule W02);

    % DET: points Ec and Mb are not the same

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

    % DET: points Ea and Ec are not the same

  3. Using the point Ea and the point Mb, construct a line m(EaMb) (rule W14);

    % DET: points Ea and Mb are not the same

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

    % NDG: lines m(EaMb) and m(EaEc) are not parallel

    % DET: lines m(EaMb) and m(EaEc) are not the same

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

    % NDG: points Ea and N are not the same

  6. Using the point Ea and the line m(CHa), construct a line ha (rule W16);

  7. Using the circle k(N,Ma), the line ha, the point N and the point Ea, construct a point Ha (rule W05);

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

    % DET: points Ea and Ha must be different

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

    % NDG: points Ha and Ec are not the same

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

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

    % DET: points Ha and H must be different

  10. Using the point H and the point Ea, construct a point A (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 Mb and the point G, construct a point B (rule W01);

animation
Construction in GCLC language

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