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Problem 384 from Wernick's corpus: Ma, Hc, Tc


Problem

Given a point Ma, a point Hc and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Hc and the point Tc, construct a line c (rule W02);

    % DET: points Hc and Tc are not the same

  2. 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

  3. Using the circle k(Ma,B), the line c, the point Ma and the point Hc, construct a point B (rule W05);

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

    % DET: points Hc and B must be different

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

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

    % DET: points Ma and B are not the same

  6. Using the point Tc and the line a, construct a circle k(Tc,foot[Tc,b]) (rule W11);

    % NDG: point Tc is not incident to the line a

  7. Using the circle k(Tc,foot[Tc,b]), the point C, the point Tc and the line a, construct a line b (rule W13);

    % NDG: point C is outside the circle k(Tc,foot[Tc,b])

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

    % NDG: lines b and c are not parallel

    % DET: lines b and c are not the same

animation
Construction in GCLC language

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