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Problem 30 from Connelly's corpus: A, Eb, Hc


Problem

Given a point A, a point Eb and a point Hc, 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 Hc, construct a line c (rule W02);

    % DET: points A and Hc are not the same

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

    % NDG: points Hc and Eb are not the same

  3. Using the circle k(Eb,B), the line c, the point Eb and the point Hc, construct a point B (rule W05);

    % NDG: line c and circle k(Eb,B) intersect

    % DET: points Hc and B must be different

  4. Using the point Eb and the point B, construct a point H (rule W01);

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

    % DET: points A and H are not the same

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

    % DET: points Hc and H are not the same

  7. Using the circle k(Eb,B), the line ha, the point Eb and the point H, construct a point Ha (rule W05);

    % NDG: line ha and circle k(Eb,B) intersect

    % DET: points H and Ha must be different

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

    % DET: points B and Ha are not the same

  9. Using the line hc and the line a, construct a point C (rule W03);

    % NDG: lines hc and a are not parallel

    % DET: lines hc and a are not the same

animation
Construction in GCLC language

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