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Problem 226 from Wernick's corpus: C, Mb, Ta


Problem

Given a point C, a point Mb and a point Ta, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

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

    % DET: points C and Mb are not the same

  3. Using the point C and the point Ta, construct a line a (rule W02);

    % DET: points C and Ta are not the same

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

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

  5. Using the circle k(Ta,foot[Ta,c]), the point A, the point Ta and the line b, construct a line c (rule W13);

    % NDG: point A is outside the circle k(Ta,foot[Ta,c])

  6. 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

 animation
Construction in GCLC language

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