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Problem 178 from Connelly's corpus: C, Hc, N


Problem

Given a point C, a point Hc 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 C and the point Hc, construct a line hc (rule W02);

    % DET: points C and Hc are not the same

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

    % NDG: points Hc and N are not the same

  3. Using the circle k(N,Ma), the line hc, the point N and the point Hc, construct a point Ec (rule W05);

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

    % DET: points Hc and Ec must be different

  4. Using the point Ec and the point C, construct a point H (rule W01);

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

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

  7. Using the point C and the point G, construct a point Mc (rule W01);

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

    % DET: points Hc and Mc are not the same

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

    % NDG: points C and O are not the same

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

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

animation
Construction in GCLC language

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