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Problem 412 from Wernick's corpus: Mb, G, I


Problem

Given a point Mb, a point G 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 G, construct a point B (rule W01);

  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 B, construct a line sb (rule W02);

    % DET: points I and B are not the same

  4. 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

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

  6. Using the point Mb, the line BP`b and the point B, construct a line hMb,-1/1(BP`b) (rule W15);

  7. Using the circle k_over(I,Mb) and the line hMb,-1/1(BP`b), construct a point Bfo and a point Pb (rule W04);

    % NDG: line hMb,-1/1(BP`b) and circle k_over(I,Mb) intersect

  8. Using the point Pb and the point I, construct a circle k(I,Pa) (rule W06);

    % NDG: points Pb and I are not the same

  9. Using the circle k(I,Pa), the point Mb and the point I, construct a line x2 and a line b (rule W12);

    % NDG: point Mb is outside the circle k(I,Pa)

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

  11. 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

  12. 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

  13. 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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