Back to the list of problems

Problem 466 from Wernick's corpus: Mc, Hc, I


Problem

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

    % DET: points Mc and Hc are not the same

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

    % DET: points Mc and I are not the same

  3. Using the point I and the point Mc, construct a circle k_over(I,Mc) (rule W09);

    % NDG: points I and Mc are not the same

  4. Using the point Mc and the line c, construct a line mc (rule W10b);

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

  6. 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

  7. Using the circle k(I,Pa) and the circle k_over(I,Mc), construct a point Cfi and a point Pc (rule W07);

    % NDG: circles k(I,Pa) and k_over(I,Mc) intersect

    % DET: circles k(I,Pa) and k_over(I,Mc) are not the same

  8. Using the point Pc and the point Mc, construct a point P`c (rule W01);

  9. Using the point P`c and the line IMc, construct a line CP`c (rule W16);

  10. Using the line CP`c and the line hc, construct a point C (rule W03);

    % NDG: lines CP`c and hc are not parallel

    % DET: lines CP`c and hc are not the same

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

    % DET: points I and C are not the same

  12. Using the line mc and the line sc, construct a point Nc (rule W03);

    % NDG: lines mc and sc are not parallel

    % DET: lines mc and sc are not the same

  13. Using the point I and the point Nc, construct a circle k(Nc,B) (rule W06);

    % NDG: points I and Nc are not the same

  14. Using the circle k(Nc,B) and the line c, construct a point B and a point A (rule W04);

    % NDG: line c and circle k(Nc,B) intersect

animation
Construction in GCLC language

Back to the list of problems