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Problem 6 from Connelly's corpus: A, C, Eb


Problem

Given a point A, a point C and a point Eb, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point A and the point C, construct a point Mb (rule W01);

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

    % DET: points A and C are not the same

  3. Using the point Eb and the point Mb, construct a line m(HaHc) (rule W02);

    % DET: points Eb and Mb are not the same

  4. Using the point Eb and the line b, construct a line hb (rule W10b);

  5. Using the line hb and the line b, construct a point Hb (rule W03);

    % NDG: lines hb and b are not parallel

    % DET: lines hb and b are not the same

  6. Using the point A and the point Hb, construct a line m(AHb) (rule W14);

    % DET: points A and Hb are not the same

  7. Using the point Eb and the point Mb, construct a line m(EbMb) (rule W14);

    % DET: points Eb and Mb are not the same

  8. Using the line m(EbMb) and the line m(HaHc), construct a point N (rule W03);

    % NDG: lines m(EbMb) and m(HaHc) are not parallel

    % DET: lines m(EbMb) and m(HaHc) are not the same

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

    % NDG: points Eb and N are not the same

  10. Using the circle k(N,Ma) and the line m(AHb), construct a point Mc and a point Ea (rule W04);

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

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

animation
Construction in GCLC language

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