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Problem 381 from Wernick's corpus: Ma, Hc, H


Problem

Given a point Ma, a point Hc 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 Hc and the point H, construct a line hc (rule W02);

    % DET: points Hc and H are not the same

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

    % NDG: points Hc and Ma are not the same

  3. Using the circle k(Ma,B), the line hc, the point Ma and the point Hc, construct a point C (rule W05);

    % NDG: line hc and circle k(Ma,B) intersect

    % DET: points Hc and C must be different

  4. Using the point C and the point Ma, construct a point B (rule W01);

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

    % DET: points Hc and B are not the same

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

    % DET: points H and B are not the same

  7. Using the circle k(Ma,B), the line hb, the point Ma and the point B, construct a point Hb (rule W05);

    % NDG: line hb and circle k(Ma,B) intersect

    % DET: points B and Hb must be different

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

    % DET: points C and Hb are not the same

  9. Using the line c and the line b, construct a point A (rule W03);

    % NDG: lines c and b are not parallel

    % DET: lines c and b are not the same

animation
Construction in GCLC language

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