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Problem 367 from Wernick's corpus: Ma, G, I


Problem

Given a point Ma, 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 Ma and the point G, construct a point A (rule W01);

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

    % DET: points Ma and I are not the same

  3. Using the point I and the point A, construct a line sa (rule W02);

    % DET: points I and A are not the same

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

    % NDG: points I and Ma are not the same

  5. Using the point A and the line IMa, construct a line AP`a (rule W16);

  6. Using the point Ma, the line AP`a and the point A, construct a line hMa,-1/1(AP`a) (rule W15);

  7. Using the circle k_over(I,Ma) and the line hMa,-1/1(AP`a), construct a point Afo and a point Pa (rule W04);

    % NDG: line hMa,-1/1(AP`a) and circle k_over(I,Ma) intersect

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

    % NDG: points Pa and I are not the same

  9. Using the circle k(I,Pa), the point Ma and the point I, construct a line x1 and a line a (rule W12);

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

  10. Using the point Ma and the line a, construct a line ma (rule W10b);

  11. Using the line ma and the line sa, construct a point Na (rule W03);

    % NDG: lines ma and sa are not parallel

    % DET: lines ma and sa are not the same

  12. Using the point I and the point Na, construct a circle k(Na,C) (rule W06);

    % NDG: points I and Na are not the same

  13. Using the circle k(Na,C) and the line a, construct a point C and a point B (rule W04);

    % NDG: line a and circle k(Na,C) intersect

 animation
Construction in GCLC language

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