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Problem 270 from Wernick's corpus: C, Ta, Tc


Problem

Given a point C, a point Ta 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 Ta, construct a line a (rule W02);

    % DET: points C and Ta are not the same

  2. 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

  3. 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])

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

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

  5. Using the circle k(Ta,foot[Ta,c]), the point Tc and the point Ta, construct a line c1 and a line c (rule W12);

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

  6. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a 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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