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Problem 540 from Connelly's corpus: Hb, Mc, N


Problem

Given a point Hb, a point Mc 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 Mc and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Mc and N are not the same

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

  3. Using the point Hb and the point Mc, construct a circle k(Mc,A) (rule W06);

    % NDG: points Hb and Mc are not the same

  4. Using the circle k(N,Ma), the circle k(Mc,A), the point Hb, the point N and the point Mc, construct a point Ha (rule W08);

    % NDG: circles k(N,Ma) and k(Mc,A) intersect

    % DET: circles k(N,Ma) and k(Mc,A) are not the same points Hb and Ha must be different

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

  6. Using the point A and the point Mc, construct a point B (rule W01);

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

    % DET: points A and Hb are not the same

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

    % DET: points Ha and B are not the same

  9. Using the line b and the line a, construct a point C (rule W03);

    % NDG: lines b and a are not parallel

    % DET: lines b and a are not the same

animation
Construction in GCLC language

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