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Problem 550 from Wernick's corpus: Hc, Tc, I


Problem

Given a point Hc, a point Tc 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 Hc and the point Tc, construct a line c (rule W02);

    % DET: points Hc and Tc are not the same

  2. Using the point Tc and the point I, construct a line sc (rule W02);

    % DET: points Tc and I are not the same

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

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

    % NDG: lines hc and sc are not parallel

    % DET: lines hc and sc are not the same

  5. 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

  6. Using the circle k(I,Pa), the point C and the point I, construct a line a and a line b (rule W12);

    % 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

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

    % NDG: lines c and b are not parallel

    % DET: lines c and b are not the same

animation
Construction in GCLC language

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