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Problem 37 from Wernick's corpus: A, O, Tb


Problem

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

    % DET: points A and Tb are not the same

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

    % NDG: points A and O are not the same

  3. Using the circle k(O,C), the line b, the point O and the point A, construct a point C (rule W05);

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

    % DET: points A and C must be different

  4. Using the point C and the point A, construct a point Mb (rule W01);

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

    % DET: points O and Mb are not the same

  6. Using the circle k(O,C) and the line mb, construct a point Nb and a point Nbk (rule W04);

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

  7. Using the point Nb and the point Tb, construct a line sb (rule W02);

    % DET: points Nb and Tb are not the same

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

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

    % DET: points Nb and B must be different

animation
Construction in GCLC language

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