Back to the list of problems

Problem 83 from Wernick's corpus: A, Ha, Tc


Problem

Given a point A, a point Ha and a point Tc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point A and the point Ha, construct a line ha (rule W02);

    % DET: points A and Ha are not the same

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

    % DET: points A and Tc are not the same

  3. Using the point Ha and the line ha, construct a line a (rule W10a);

  4. 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

  5. Using the point A, the point B, the point Tc and the line c, construct a point T`c (rule W19);

    % NDG: points A and B are not the same points B and Tc are not the same points B and midpoint([A,Tc]) are not the same

  6. Using the point Tc and the point T`c, construct a circle k_over(Tc,T`c) (rule W09);

    % NDG: points Tc and T`c are not the same

  7. Using the circle k_over(Tc,T`c) and the line a, construct a point Cwb and a point C (rule W04);

    % NDG: line a and circle k_over(Tc,T`c) intersect

animation
Construction in GCLC language

Back to the list of problems