Back to the list of problems

Problem 27 from Connelly's corpus: A, Eb, H


Problem

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

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

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

    % DET: points A and B are not the same

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

    % DET: points Eb 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 c, the point Ea and the point A, construct a point Hc (rule W05);

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

    % DET: points A 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(Ea,A), the line hb, the point Ea and the point H, construct a point Hb (rule W05);

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

    % DET: points H and Hb must be different

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

    % DET: points Hb and A are not the same

  10. Using the line hc and the line b, construct a point C (rule W03);

    % NDG: lines hc and b are not parallel

    % DET: lines hc and b are not the same

animation
Construction in GCLC language

Back to the list of problems