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Problem 376 from Wernick's corpus: Ma, Hb, H


Problem

Given a point Ma, a point Hb 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 Hb and the point H, construct a line hb (rule W02);

    % DET: points Hb and H are not the same

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

    % NDG: points Hb and Ma are not the same

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

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

    % DET: points Hb and B must be different

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

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

    % DET: points Hb and C are not the same

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

    % DET: points H and C are not the same

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

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

    % DET: points C and Hc must be different

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

    % DET: points B and Hc are not the same

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

    % NDG: lines b and c are not parallel

    % DET: lines b and c are not the same

animation
Construction in GCLC language

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