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Problem 438 from Connelly's corpus: Ec, Ha, Hc


Problem

Given a point Ec, a point Ha 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 Ec and the point Hc, construct a line hc (rule W02);

    % DET: points Ec and Hc are not the same

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

    % NDG: points Ha and Ec are not the same

  3. Using the circle k(Ec,C) and the line hc, construct a point C and a point H (rule W04);

    % NDG: line hc and circle k(Ec,C) intersect

  4. Using the point Ha and the point C, construct a line a (rule W02);

    % DET: points Ha and C are not the same

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

    % DET: points Ha and H are not the same

  6. Using the point Hc and the line hc, construct a line c (rule W10a);

  7. Using the line c and the line a, construct a point B (rule W03);

    % NDG: lines c and a are not parallel

    % DET: lines c and a are not the same

  8. 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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