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Problem 77 from Connelly's corpus: B, Ea, Hc


Problem

Given a point B, a point Ea 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 B and the point Hc, construct a line c (rule W02);

    % DET: points B and Hc are not the same

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

    % NDG: points Hc and Ea are not the same

  3. Using the circle k(Ea,A), the line c, the point Ea and the point Hc, construct a point A (rule W05);

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

    % DET: points Hc and A must be different

  4. Using the point Ea and the point A, construct a point H (rule W01);

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

    % DET: points B and H are not the same

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

    % DET: points Hc and H are not the same

  7. 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

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

    % DET: points A and Hb are not the same

  9. 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

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