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Problem 92 from Wernick's corpus: A, Hc, Ta


Problem

Given a point A, a point Hc and a point Ta, 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 Hc, construct a line c (rule W02);

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

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

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

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

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

    % NDG: lines b and hc are not parallel

    % DET: lines b and hc are not the same

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

    % DET: points Ta and C are not the same

  7. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

animation
Construction in GCLC language

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