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Problem 140 from Connelly's corpus: C, Ea, N


Problem

Given a point C, a point Ea and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Ea and N are not the same

  2. 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

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

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

    % DET: points Ea and Ma must be different

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

  5. Using the point C and the point Ma, construct a line a (rule W02);

    % DET: points C and Ma are not the same

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

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

    % DET: points Ma and Ha must be different

  7. Using the point Ha and the point Ea, construct a line ha (rule W02);

    % DET: points Ha and Ea are not the same

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

    % NDG: points C and Ma are not the same

  9. Using the circle k(N,Ma) and the circle k(Ma,B), construct a point Hb and a point Hc (rule W07);

    % NDG: circles k(N,Ma) and k(Ma,B) intersect

    % DET: circles k(N,Ma) and k(Ma,B) are not the same

  10. Using the point C and the point Hb, construct a line b (rule W02);

    % DET: points C and Hb are not the same

  11. Using the line ha and the line b, construct a point A (rule W03);

    % NDG: lines ha and b are not parallel

    % DET: lines ha and b are not the same

animation
Construction in GCLC language

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