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Problem 182 from Connelly's corpus: C, Mc, N


Problem

Given a point C, a point Mc 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 Mc, construct a point G (rule W01);

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

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

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

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

    % DET: points C and H are not the same

  6. 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

  7. 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

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

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

    % DET: points Ec and Hc must be different

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

    % DET: points Hc and Mc 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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