Problem 282 from Wernick's corpus: O, Ma, Ta


Problem

Given a point O, a point Ma and a point Ta, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Ma and the point Ta, construct a line a (rule W02);

    % DET: points Ma and Ta are not the same

  2. Using the point Ma and the line a, construct a line ma (rule W10b);

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

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

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

  6. 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

  7. 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

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

    % DET: points Na and Ta are not the same

  9. 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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