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Problem 428 from Wernick's corpus: Mb, Hc, Tb


Problem

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

    % DET: points Mb and Tb are not the same

  2. Using the point Hc and the point Mb, construct a circle k(Mb,C) (rule W06);

    % NDG: points Hc and Mb are not the same

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

    % NDG: line b and circle k(Mb,C) intersect

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

    % DET: points Hc and A 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 c, construct a point Bwa and a point B (rule W04);

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

animation
Construction in GCLC language

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