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Problem 415 from Wernick's corpus: Mb, Ha, H


Problem

Given a point Mb, a point Ha 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 Ha and the point H, construct a line ha (rule W02);

    % DET: points Ha and H are not the same

  2. Using the point Ha and the point Mb, construct a circle k(Mb,C) (rule W06);

    % NDG: points Ha and Mb are not the same

  3. Using the circle k(Mb,C), the line ha, the point Mb and the point Ha, construct a point A (rule W05);

    % NDG: line ha and circle k(Mb,C) intersect

    % DET: points Ha and A must be different

  4. Using the point A and the point Mb, construct a point C (rule W01);

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

    % DET: points Ha 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(Mb,C), the line hc, the point Mb and the point C, construct a point Hc (rule W05);

    % NDG: line hc and circle k(Mb,C) intersect

    % DET: points C and Hc must be different

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

    % DET: points A and Hc are not the same

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

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

animation
Construction in GCLC language

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