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Problem 392 from Wernick's corpus: Ma, Ta, I


Problem

Given a point Ma, a point Ta 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 Ta, construct a line a (rule W02);

    % DET: points Ma and Ta are not the same

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

    % DET: points Ta and I are not the same

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

  4. 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

  5. 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

  6. 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

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

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

  8. Using the circle k(I,Pa), the point C, the point I and the line a, construct a line b (rule W13);

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

  9. Using the line b and the line sa, construct a point A (rule W03);

    % NDG: lines b and sa are not parallel

    % DET: lines b and sa are not the same

animation
Construction in GCLC language

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