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Problem 127 from Wernick's corpus: B, O, Ta


Problem

Given a point B, 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 B and the point Ta, construct a line a (rule W02);

    % DET: points B and Ta 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 a, the point O and the point B, construct a point C (rule W05);

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

    % DET: points B and C must be different

  4. Using the point C and the point B, construct a point Ma (rule W01);

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

    % DET: points O and Ma are not the same

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

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

  7. Using the point Na and the point Ta, construct a line sa (rule W02);

    % DET: points Na and Ta are not the same

  8. Using the circle k(O,C), the line sa, the point O and the point Na, construct a point A (rule W05);

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

    % DET: points Na and A must be different

animation
Construction in GCLC language

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