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Problem 280 from Wernick's corpus: O, Ma, Hc


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points O and Ma are not the same

  2. Using the point Hc and the point Ma, construct a circle k(Ma,B) (rule W06);

    % NDG: points Hc and Ma are not the same

  3. Using the point Ma and the line ma, construct a line a (rule W10a);

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

    % NDG: line a and circle k(Ma,B) intersect

  5. Using the point Hc and the point B, construct a line c (rule W02);

    % DET: points Hc and B are not the same

  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), the line c, the point O and the point B, construct a point A (rule W05);

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

    % DET: points B and A must be different

animation
Construction in GCLC language

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