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Problem 475 from Connelly's corpus: Ec, Ma, Mb


Problem

Given a point Ec, a point Ma 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 Ma, construct a line m(EcMa) (rule W14);

    % DET: points Ec and Ma are not the same

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

    % DET: points Ec and Mb are not the same

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

    % NDG: lines m(EcMb) and m(EcMa) are not parallel

    % DET: lines m(EcMb) and m(EcMa) 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 Ec and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Ec 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 Mb and the point Ea, construct a line m(AHc) (rule W02);

    % DET: points Mb and Ea are not the same

  8. Using the point Ec and the line m(AHc), construct a line hc (rule W16);

  9. Using the circle k(N,Ma), the line hc, the point N and the point Ec, construct a point Hc (rule W05);

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

    % DET: points Ec and Hc must be different

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

    % NDG: points Hc and Ma are not the same

  11. Using the circle k(Ma,B), the line hc, the point Ma and the point Hc, construct a point C (rule W05);

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

    % DET: points Hc and C must be different

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

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

animation
Construction in GCLC language

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