Back to the list of problems

Problem 184 from Wernick's corpus: B, Hc, Tb


Problem

Given a point B, a point Hc and a point Tb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point B and the point Hc, construct a line c (rule W02);

    % DET: points B 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 Tb and the line c, construct a circle k(Tb,foot[Tb,c]) (rule W11);

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

  4. Using the circle k(Tb,foot[Tb,c]), the point B, the point Tb and the line c, construct a line a (rule W13);

    % NDG: point B is outside the circle k(Tb,foot[Tb,c])

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

    % NDG: lines a and hc are not parallel

    % DET: lines a and hc are not the same

  6. Using the point Tb and the point C, construct a line b (rule W02);

    % DET: points Tb and C are not the same

  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

animation
Construction in GCLC language

Back to the list of problems