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Problem 90 from Wernick's corpus: A, Hb, I


Problem

Given a point A, a point Hb 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 Hb, construct a line b (rule W02);

    % DET: points A and Hb are not the same

  2. Using the point Hb and the line b, construct a line hb (rule W10b);

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

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

  4. Using the circle k(I,Pa), the point A, the point I and the line b, construct a line c (rule W13);

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

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

    % NDG: lines c and hb are not parallel

    % DET: lines c and hb are not the same

  6. Using the circle k(I,Pa), the point B, the point I and the line c, construct a line a (rule W13);

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

  7. 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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