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Problem 95 from Wernick's corpus: A, Hc, I


Problem

Given a point A, a point Hc 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 Hc, construct a line c (rule W02);

    % DET: points A and Hc are not the same

  2. Using the point Hc and the line c, construct a line hc (rule W10b);

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

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

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

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

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

    % NDG: lines b and hc are not parallel

    % DET: lines b and hc are not the same

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

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

  7. 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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