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Problem 10 from Connelly's corpus: A, Ea, Ec


Problem

Given a point A, a point Ea and a point Ec, 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 Ea, construct a point H (rule W01);

  2. Using the point Ec and the point H, construct a point C (rule W01);

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

    % DET: points A and C are not the same

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

    % DET: points Ec and H are not the same

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

    % NDG: points A and Ea are not the same

  6. Using the circle k(Ea,A), the line b, the point Ea and the point A, construct a point Hb (rule W05);

    % NDG: line b and circle k(Ea,A) intersect

    % DET: points A and Hb must be different

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

    % DET: points Hb and H are not the same

  8. Using the circle k(Ea,A), the line hc, the point Ea and the point H, construct a point Hc (rule W05);

    % NDG: line hc and circle k(Ea,A) intersect

    % DET: points H and Hc must be different

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

    % DET: points Hc and A are not the same

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

    % NDG: lines hb and c are not parallel

    % DET: lines hb and c are not the same

animation
Construction in GCLC language

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