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Problem 50 from Wernick's corpus: A, Ma, I


Problem

Given a point A, a point Ma 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 I, construct a line IMa (rule W02);

    % DET: points Ma and I are not the same

  2. 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

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

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

  5. 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

  6. 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

  7. Using the circle k(I,Pa), the point A and the point I, construct a line c and a line b (rule W12);

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

  8. 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)

  9. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

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

animation
Construction in GCLC language

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