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Problem 323 from Connelly's corpus: Eb, G, Hb


Problem

Given a point Eb, a point G and a point Hb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Eb and Hb are not the same

  2. Using the point Hb and the line hb, construct a line b (rule W10a);

  3. Using the point G, the line hb and the point Eb, construct a line hG,-1/2(hb) (rule W15);

  4. Using the line hG,-1/2(hb) and the line b, construct a point Mb (rule W03);

    % NDG: lines hG,-1/2(hb) and b are not parallel

    % DET: lines hG,-1/2(hb) and b are not the same

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

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

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

  8. 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

  9. 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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