Problem 375 from Wernick's corpus: Hb, Ma, Hc


Problem

Given a point Hb, a point Ma and a point Hc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


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

    % NDG: points Hc and Ma are not the same

  2. Choose freely a point Hb on the circle k(Ma,B) (rule WOncircle)

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

    % DET: points Hb and Ma 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 m(HbHc) and the line m(HbMa), construct a point N (rule W03);

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

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

  6. Choose freely a point B on the circle k(Ma,B) (rule WOncircle)

  7. Using the point B and the point Ma, construct a point C (rule W01);

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

    % DET: points B and Hb are not the same

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

    % DET: points Hc and C are not the same

  10. Using the line hb and the line hc, construct a point H (rule W03);

    % NDG: lines hb and hc are not parallel

    % DET: lines hb and hc are not the same

  11. Using the point N and the point H, construct a point G (rule W01);

  12. Using the point Ma and the point G, construct a point A (rule W01);

animation
Construction in GCLC language

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