Back to the list of problems

Problem 225 from Wernick's corpus: C, Mb, H


Problem

Given a point C, a point Mb 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 C and the point Mb, construct a point A (rule W01);

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

    % DET: points C and H are not the same

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

    % DET: points H and A are not the same

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

    % NDG: points C and Mb are not the same

  5. Using the circle k(Mb,C), the line hc, the point Mb and the point C, construct a point Hc (rule W05);

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

    % DET: points C and Hc must be different

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

    % DET: points Hc and A are not the same

  7. 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

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

    % DET: points Ha and C are not the same

  9. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

animation
Construction in GCLC language

Back to the list of problems