Back to the list of problems

Problem 439 from Wernick's corpus: Mb, Tb, I


Problem

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

    % DET: points Mb 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 Mb and the line b, construct a line mb (rule W10b);

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

    % NDG: lines mb and sb are not parallel

    % DET: lines mb and sb are not the same

  5. Using the point I and the point Nb, construct a circle k(Nb,A) (rule W06);

    % NDG: points I and Nb are not the same

  6. Using the circle k(Nb,A) and the line b, construct a point A and a point C (rule W04);

    % NDG: line b and circle k(Nb,A) intersect

  7. 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

  8. 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)

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

    % NDG: lines c and sb are not parallel

    % DET: lines c and sb are not the same

animation
Construction in GCLC language

Back to the list of problems