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Problem 236 from Connelly's corpus: Ea, H, N


Problem

Given a point Ea, a point H and a point N, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

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

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

  4. Using the point A and the point G, construct a point Ma (rule W01);

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

    % DET: points Ea and H are not the same

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

    % NDG: points Ea and N are not the same

  7. Using the circle k(N,Ma), the line ha, the point N and the point Ea, construct a point Ha (rule W05);

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

    % DET: points Ea and Ha must be different

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

    % DET: points Ha and Ma are not the same

  9. 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

  10. 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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