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Problem 148 from Connelly's corpus: C, Eb, Ha


Problem

Given a point C, a point Eb and a point Ha, 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 Ha, construct a line a (rule W02);

    % DET: points C and Ha are not the same

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

    % NDG: points Ha and Eb are not the same

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

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

    % DET: points Ha and B must be different

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

    % DET: points Ha and H are not the same

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

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

    % DET: points H and Hc must be different

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

    % DET: points B and Hc are not the same

  9. Using the line ha and the line c, construct a point A (rule W03);

    % NDG: lines ha and c are not parallel

    % DET: lines ha and c are not the same

animation
Construction in GCLC language

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