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Problem 505 from Wernick's corpus: Ha, Hb, Hc


Problem

Given a point Ha, a point Hb 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 Ha and the point Hb, construct a line HaHb (rule W02);

    % DET: points Ha and Hb are not the same

  2. Using the point Ha and the point Hc, construct a line HcHa (rule W02);

    % DET: points Ha and Hc are not the same

  3. Using the point Ha and the point Hb, construct a line m(HaHb) (rule W14);

    % DET: points Ha and Hb are not the same

  4. Using the point Hb and the point Hc, construct a line m(HbHc) (rule W14);

    % DET: points Hb and Hc are not the same

  5. Using the line HcHa, the point Hb, the point Ha, the point Hc and the line HaHb, construct a line ha (rule W17);

    % NDG: points Ha and Hc are not the same points Hb and Ha are not the same

    % DET: points Ha and Hb are not the same

  6. Using the point Ha and the line ha, construct a line a (rule W10a);

  7. Using the line a and the line m(HbHc), construct a point Ma (rule W03);

    % NDG: lines a and m(HbHc) are not parallel

    % DET: lines a and m(HbHc) are not the same

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

    % NDG: points Hb and Ma are not the same

  9. 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

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

    % DET: points Hc and B are not the same

  11. Using the line m(HaHb) and the line c, construct a point Mc (rule W03);

    % NDG: lines m(HaHb) and c are not parallel

    % DET: lines m(HaHb) and c are not the same

  12. Using the point Mc and the point B, construct a point A (rule W01);

animation
Construction in GCLC language

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