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Problem 38 from Wernick's corpus: A, O, Tc


Problem

Given a point A, a point O 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 A and the point Tc, construct a line c (rule W02);

    % DET: points A and Tc 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 c, the point O and the point A, construct a point B (rule W05);

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

    % DET: points A and B must be different

  4. Using the point B and the point A, construct a point Mc (rule W01);

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

    % DET: points O and Mc are not the same

  6. Using the circle k(O,C) and the line mc, construct a point Nc and a point Nck (rule W04);

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

  7. Using the point Nc and the point Tc, construct a line sc (rule W02);

    % DET: points Nc and Tc are not the same

  8. Using the circle k(O,C), the line sc, the point O and the point Nc, construct a point C (rule W05);

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

    % DET: points Nc and C must be different

animation
Construction in GCLC language

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