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Problem 290 from Wernick's corpus: O, Mb, Hc


Problem

Given a point O, a point Mb and a point Hc, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point O and the point Mb, construct a line mb (rule W02);

    % DET: points O and Mb 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 point Mb and the line mb, construct a line b (rule W10a);

  4. 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

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

    % DET: points Hc and A are not the same

  6. Using the point C and the point O, construct a circle k(O,C) (rule W06);

    % NDG: points C and O are not the same

  7. Using the circle k(O,C), the line c, the point O and the point A, construct a point B (rule W05);

    % NDG: line c and circle k(O,C) intersect

    % DET: points A and B must be different

animation
Construction in GCLC language

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