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Problem 487 from Wernick's corpus: G, Hb, Tb


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Hb and Tb are not the same

  2. Using the point Hb and the line b, construct a line hb (rule W10b);

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

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

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

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

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

  6. Using the point Tb and the point B, construct a line sb (rule W02);

    % DET: points Tb and B are not the same

  7. Using the point Mb and the line b, construct a line mb (rule W10b);

  8. Using the line mb and the line sb, construct a point Nb (rule W03);

    % NDG: lines mb and sb are not parallel

    % DET: lines mb and sb are not the same

  9. Using the point B and the point Nb, construct a line m(BNb) (rule W14);

    % DET: points B and Nb are not the same

  10. Using the line m(BNb) and the line mb, construct a point O (rule W03);

    % NDG: lines m(BNb) and mb are not parallel

    % DET: lines m(BNb) and mb are not the same

  11. 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

  12. 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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