Back to the list of problems

Problem 326 from Wernick's corpus: O, Hc, H


Problem

Given a point O, a point Hc 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 Hc and the point H, construct a line hc (rule W02);

    % DET: points Hc and H are not the same

  3. Using the point Hc and the line hc, construct a line c (rule W10a);

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

  5. Using the line mc and the line c, construct a point Mc (rule W03);

    % NDG: lines mc and c are not parallel

    % DET: lines mc and c are not the same

  6. Using the point Mc and the point G, construct a point C (rule W01);

  7. 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

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

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

animation
Construction in GCLC language

Back to the list of problems