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Problem 100 from Wernick's corpus: A, Ta, Tb


Problem

Given a point A, a point Ta 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 A and the point Tb, construct a line b (rule W02);

    % DET: points A and Tb are not the same

  2. 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

  3. Using the circle k(Ta,foot[Ta,c]), the point A, the point Ta and the line b, construct a line c (rule W13);

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

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

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

  5. Using the circle k(Tb,foot[Tb,c]), the point Ta and the point Tb, construct a line a1 and a line a (rule W12);

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

  6. Using the line a and the line b, construct a point C (rule W03);

    % NDG: lines a and b are not parallel

    % DET: lines a and b are not the same

  7. 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

animation
Construction in GCLC language

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