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Problem 258 from Wernick's corpus: C, Hb, Tc


Problem

Given a point C, a point Hb 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 C and the point Hb, construct a line b (rule W02);

    % DET: points C and Hb are not the same

  2. Using the point Hb and the line b, construct a line hb (rule W10b);

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

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

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

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

  5. Using the line a and the line hb, construct a point B (rule W03);

    % NDG: lines a and hb are not parallel

    % DET: lines a and hb are not the same

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

    % DET: points Tc and B are not the same

  7. 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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