Problem 421 from Wernick's corpus: Mb, Hb, H


Problem

Given a point Mb, a point Hb and a point H, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


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

    % DET: points Hb and H are not the same

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

  3. Choose freely a point Mb on the line b (rule WOnline2)

  4. Choose freely a point A on the line b (rule WOnline1)

  5. Using the point A and the point Mb, construct a point C (rule W01);

  6. Using the point A and the point H, construct a line ha (rule W02);

    % DET: points A and H are not the same

  7. Using the point A and the point Mb, construct a circle k(Mb,C) (rule W06);

    % NDG: points A and Mb are not the same

  8. Using the circle k(Mb,C), the line ha, the point Mb and the point A, construct a point Ha (rule W05);

    % NDG: line ha and circle k(Mb,C) intersect

    % DET: points A and Ha must be different

  9. Using the point C and the point Ha, construct a line a (rule W02);

    % DET: points C and Ha are not the same

  10. Using the line hb and the line a, construct a point B (rule W03);

    % NDG: lines hb and a are not parallel

    % DET: lines hb and a are not the same

animation
Construction in GCLC language

Back to the list of problems