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Problem 173 from Wernick's corpus: B, Ha, Tb


Problem

Given a point B, a point Ha 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 B and the point Ha, construct a line a (rule W02);

    % DET: points B and Ha are not the same

  2. Using the point Ha and the line a, construct a line ha (rule W10b);

  3. 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

  4. 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])

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

    % NDG: lines c and ha are not parallel

    % DET: lines c and ha are not the same

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

    % DET: points Tb and A are not the same

  7. 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

animation
Construction in GCLC language

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