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Problem 321 from Wernick's corpus: O, Hb, H


Problem

Given a point O, a point Hb and a point H, 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 H, construct a point G (rule W01);

  2. Using the point Hb and the point H, construct a line hb (rule W02);

    % DET: points Hb and H are not the same

  3. Using the point Hb and the line hb, construct a line b (rule W10a);

  4. Using the point O and the line b, construct a line mb (rule W10b);

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

    % NDG: lines mb and b are not parallel

    % DET: lines mb and b are not the same

  6. Using the point Mb and the point G, construct a point B (rule W01);

  7. 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

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

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

animation
Construction in GCLC language

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