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Problem 74 from Connelly's corpus: B, Ea, H


Problem

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

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


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

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

  3. Using the point B and the point A, construct a line c (rule W02);

    % DET: points B and A are not the same

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

    % DET: points Ea and H are not the same

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

    % NDG: points B and Eb are not the same

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

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

    % DET: points B and Hc must be different

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

    % DET: points Hc and H are not the same

  8. 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

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

    % DET: points Ha and B are not the same

  10. 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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