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Problem 98 from Connelly's corpus: B, Eb, O


Problem

Given a point B, a point Eb and a point O, 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 Eb, construct a point H (rule W01);

  2. Using the point O and the point H, construct a point N (rule W01);

  3. Using the point O and the point H, construct a point G (rule W01);

  4. Using the point B and the point G, construct a point Mb (rule W01);

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

    % DET: points B and Eb 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 point Eb and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Eb and N are not the same

  8. Using the circle k(N,Ma), the line hb, the point N and the point Eb, construct a point Hb (rule W05);

    % NDG: line hb and circle k(N,Ma) intersect

    % DET: points Eb and Hb must be different

  9. Using the point Hb and the point Mb, construct a line b (rule W02);

    % DET: points Hb and Mb are not the same

  10. Using the circle k(O,C) and the line b, construct a point C and a point A (rule W04);

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

animation
Construction in GCLC language

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