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Problem 430 from Connelly's corpus: Ec, H, Mb


Problem

Given a point Ec, a point H and a point Mb, 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 H, construct a point C (rule W01);

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

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

    % DET: points H and A are not the same

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

    % DET: points Mb and C are not the same

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

    % NDG: points H and Ec are not the same

  6. Using the circle k(Ec,C), the line ha, the point Ec and the point H, construct a point Ha (rule W05);

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

    % DET: points H and Ha must be different

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

    % DET: points Ha and C are not the same

  8. Using the circle k(Ec,C), the line b, the point Ec and the point C, construct a point Hb (rule W05);

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

    % DET: points C and Hb must be different

  9. Using the point Hb and the point H, construct a line hb (rule W02);

    % DET: points Hb and H are not the same

  10. Using the line a and the line hb, construct a point B (rule W03);

    % NDG: lines a and hb are not parallel

    % DET: lines a and hb are not the same

animation
Construction in GCLC language

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