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Problem 145 from Connelly's corpus: C, Eb, Ec


Problem

Given a point C, a point Eb and a point Ec, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point C and the point Ec, construct a point H (rule W01);

  2. Using the point Eb and the point H, construct a point B (rule W01);

  3. Using the point C and the point B, construct a line a (rule W02);

    % DET: points C and B are not the same

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

    % DET: points Eb and H are not the same

  5. Using the point C and the point Ec, construct a circle k(Ec,C) (rule W06);

    % NDG: points C and Ec are not the same

  6. Using the circle k(Ec,C), the line a, the point Ec and the point C, construct a point Ha (rule W05);

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

    % DET: points C and Ha must be different

  7. Using the point Ha and the point H, construct a line ha (rule W02);

    % DET: points Ha and H are not the same

  8. Using the circle k(Ec,C), the line hb, the point Ec and the point H, construct a point Hb (rule W05);

    % NDG: line hb and circle k(Ec,C) intersect

    % DET: points H and Hb must be different

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

    % DET: points Hb and C are not the same

  10. Using the line ha and the line b, construct a point A (rule W03);

    % NDG: lines ha and b are not parallel

    % DET: lines ha and b are not the same

animation
Construction in GCLC language

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