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Problem 378 from Wernick's corpus: Ma, Hb, Tb


Problem

Given a point Ma, a point Hb and a point Tb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Hb and Tb are not the same

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

    % NDG: points Hb and Ma are not the same

  3. Using the circle k(Ma,B), the line b, the point Ma and the point Hb, construct a point C (rule W05);

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

    % DET: points Hb and C must be different

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

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

    % DET: points Ma and C are not the same

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

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

  7. Using the circle k(Tb,foot[Tb,c]), the point B, the point Tb and the line a, construct a line c (rule W13);

    % NDG: point B is outside the circle k(Tb,foot[Tb,c])

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

    % NDG: lines c and b are not parallel

    % DET: lines c and b are not the same

animation
Construction in GCLC language

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