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Problem 84 from Wernick's corpus: A, Ha, I


Problem

Given a point A, a point Ha 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 A and the point Ha, construct a line ha (rule W02);

    % DET: points A and Ha are not the same

  2. Using the point Ha and the line ha, construct a line a (rule W10a);

  3. 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

  4. 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)

  5. 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

  6. Using the line a and the line b, construct a point C (rule W03);

    % NDG: lines a and b are not parallel

    % DET: lines a and b are not the same

animation
Construction in GCLC language

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