Problem 303 from Wernick's corpus: O, Mc, Tc


Problem

Given a point O, a point Mc and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Mc and the point Tc, construct a line c (rule W02);

    % DET: points Mc and Tc are not the same

  2. Using the point Mc and the line c, construct a line mc (rule W10b);

  3. Choose freely a point O on the line mc (rule WOnline2)

  4. Choose freely a point A on the line c (rule WOnline1)

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

  6. 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

  7. 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

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

    % DET: points Nc and Tc are not the same

  9. 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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