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Problem 125 from Wernick's corpus: B, O, Hc


Problem

Given a point B, a point O 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 B and the point Hc, construct a line c (rule W02);

    % DET: points B and Hc are not the same

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

    % NDG: points B and O are not the same

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

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

    % DET: points B and A must be different

  4. Using the point Hc and the line c, construct a line hc (rule W10b);

  5. Using the circle k(O,C) and the line hc, construct a point C and a point Ck (rule W04);

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

animation
Construction in GCLC language

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