Back to the list of problems

Problem 539 from Wernick's corpus: Hb, Tb, I


Problem

Given a point Hb, a point Tb 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 Hb and the point Tb, construct a line b (rule W02);

    % DET: points Hb and Tb are not the same

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

    % DET: points Tb and I are not the same

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

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

    % NDG: lines hb and sb are not parallel

    % DET: lines hb and sb are not the same

  5. 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

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

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

  7. 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

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

    % NDG: lines b and a are not parallel

    % DET: lines b and a are not the same

animation
Construction in GCLC language

Back to the list of problems