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Problem 429 from Wernick's corpus: Mb, Hc, Tc


Problem

Given a point Mb, a point Hc and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Hc and the point Tc, construct a line c (rule W02);

    % DET: points Hc and Tc are not the same

  2. Using the point Hc and the point Mb, construct a circle k(Mb,C) (rule W06);

    % NDG: points Hc and Mb are not the same

  3. Using the circle k(Mb,C), the line c, the point Mb and the point Hc, construct a point A (rule W05);

    % NDG: line c and circle k(Mb,C) intersect

    % DET: points Hc and A must be different

  4. Using the point A and the point Mb, construct a point C (rule W01);

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

    % DET: points Mb and A are not the same

  6. Using the point Tc and the line b, construct a circle k(Tc,foot[Tc,b]) (rule W11);

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

  7. Using the circle k(Tc,foot[Tc,b]), the point C, the point Tc and the line b, construct a line a (rule W13);

    % NDG: point C is outside the circle k(Tc,foot[Tc,b])

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

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

animation
Construction in GCLC language

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