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Problem 251 from Wernick's corpus: C, Ha, Tb


Problem

Given a point C, a point Ha 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 C and the point Ha, construct a line a (rule W02);

    % DET: points C and Ha are not the same

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

    % DET: points C and Tb are not the same

  3. Using the point Ha and the line a, construct a line ha (rule W10b);

  4. Using the line ha and the line b, construct a point A (rule W03);

    % NDG: lines ha and b are not parallel

    % DET: lines ha and b are not the same

  5. Using the point A, the point C, the point Tb and the line b, construct a point T`b (rule W19);

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

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

    % NDG: points Tb and T`b are not the same

  7. Using the circle k_over(Tb,T`b) and the line a, construct a point Bwc and a point B (rule W04);

    % NDG: line a and circle k_over(Tb,T`b) intersect

animation
Construction in GCLC language

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