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Problem 425 from Wernick's corpus: Mb, Hb, I


Problem

Given a point Mb, a point Hb and a point I, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

    % DET: points Mb and Hb are not the same

  2. Using the point Mb and the point I, construct a line IMb (rule W02);

    % DET: points Mb and I are not the same

  3. Using the point I and the point Mb, construct a circle k_over(I,Mb) (rule W09);

    % NDG: points I and Mb are not the same

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

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

  6. Using the point I and the line b, construct a circle k(I,Pa) (rule W11);

    % NDG: point I is not incident to the line b

  7. Using the circle k(I,Pa) and the circle k_over(I,Mb), construct a point Bfi and a point Pb (rule W07);

    % NDG: circles k(I,Pa) and k_over(I,Mb) intersect

    % DET: circles k(I,Pa) and k_over(I,Mb) are not the same

  8. Using the point Pb and the point Mb, construct a point P`b (rule W01);

  9. Using the point P`b and the line IMb, construct a line BP`b (rule W16);

  10. Using the line BP`b and the line hb, construct a point B (rule W03);

    % NDG: lines BP`b and hb are not parallel

    % DET: lines BP`b and hb are not the same

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

    % DET: points I and B are not the same

  12. 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

  13. Using the point I and the point Nb, construct a circle k(Nb,A) (rule W06);

    % NDG: points I and Nb are not the same

  14. Using the circle k(Nb,A) and the line b, construct a point A and a point C (rule W04);

    % NDG: line b and circle k(Nb,A) intersect

animation
Construction in GCLC language

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