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Problem 128 from Wernick's corpus: B, O, Tb


Problem

Given a point B, a point O 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 Tb, construct a line sb (rule W02);

    % DET: points B and Tb are not the same

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

    % NDG: points B and O are not the same

  3. Using the circle k(O,C), the line sb, the point O and the point B, construct a point Nb (rule W05);

    % NDG: line sb and circle k(O,C) intersect

    % DET: points B and Nb must be different

  4. Using the point Nb and the point O, construct a line mb (rule W02);

    % DET: points Nb and O are not the same

  5. Using the point Tb and the line mb, construct a line b (rule W10a);

  6. Using the circle k(O,C) and the line b, construct a point C and a point A (rule W04);

    % NDG: line b and circle k(O,C) intersect

animation
Construction in GCLC language

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