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Problem 247 from Connelly's corpus: Ea, Ha, N


Problem

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

    % NDG: points Ha and N are not the same

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

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

    % DET: points Ea and Ha are not the same

  4. Using the point Ea and the point N, construct a line m(HbHc) (rule W02);

    % DET: points Ea and N are not the same

  5. Using the circle k(N,Ma), the line m(HbHc), the point N and the point Ea, construct a point Ma (rule W05a);

    % NDG: line m(HbHc) and circle k(N,Ma) intersect

    % DET: points Ea and Ma must be different

  6. Using the point Ma and the point Ha, construct a line a (rule W02);

    % DET: points Ma and Ha are not the same

  7. Choose freely a point A on the line ha (rule WOnline1)

  8. Using the point A and the point Ea, construct a point H (rule W01);

  9. Using the point N and the point H, construct a point O (rule W01);

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

    % NDG: points A and O are not the same

  11. Using the circle k(O,C) and the line a, construct a point C and a point B (rule W04);

    % NDG: line a and circle k(O,C) intersect

animation
Construction in GCLC language

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