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Problem 530 from Connelly's corpus: Ha, Mb, N


Problem

Given a point Ha, a point Mb and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is locus dependent.

Illustration

Figure of construction

Solution


  1. Using the point Mb and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Mb and N are not the same

  2. Choose freely a point Ha on the circle k(N,Ma) (rule WOncircle)

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

    % NDG: points Ha and Mb are not the same

  4. Using the circle k(N,Ma), the circle k(Mb,C), the point Ha, the point N and the point Mb, construct a point Hc (rule W08);

    % NDG: circles k(N,Ma) and k(Mb,C) intersect

    % DET: circles k(N,Ma) and k(Mb,C) are not the same points Ha and Hc must be different

  5. Choose freely a point A on the circle k(Mb,C) (rule WOncircle)

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

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

    % DET: points A and Ha are not the same

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

    % DET: points Hc and C are not the same

  9. Using the line ha and the line hc, construct a point H (rule W03);

    % NDG: lines ha and hc are not parallel

    % DET: lines ha and hc are not the same

  10. Using the point N and the point H, construct a point G (rule W01);

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

animation
Construction in GCLC language

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