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Problem 36 from Wernick's corpus: A, O, Ta


Problem

Given a point A, a point O and a point Ta, 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 Ta, construct a line sa (rule W02);

    % DET: points A and Ta 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 sa, the point O and the point A, construct a point Na (rule W05);

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

    % DET: points A and Na must be different

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

    % DET: points Na and O are not the same

  5. Using the point Ta and the line ma, construct a line a (rule W10a);

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

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

animation
Construction in GCLC language

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