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Problem 547 from Connelly's corpus: Hc, Mb, N


Problem

Given a point Hc, 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 Hc on the circle k(N,Ma) (rule WOncircle)

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

    % NDG: points Hc and Mb are not the same

  4. Using the circle k(N,Ma), the circle k(Mb,C), the point Hc, the point N and the point Mb, construct a point Ha (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 Hc and Ha 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 Hc, construct a line c (rule W02);

    % DET: points A and Hc are not the same

  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

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