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Problem 450 from Wernick's corpus: Mc, Ha, Hc


Problem

Given a point Mc, a point Ha 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 Mc and the point Hc, construct a line c (rule W02);

    % DET: points Mc and Hc are not the same

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

    % NDG: points Ha and Mc are not the same

  3. Using the circle k(Mc,A) and the line c, construct a point A and a point B (rule W04);

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

  4. Using the point Ha and the point B, construct a line a (rule W02);

    % DET: points Ha and B are not the same

  5. Using the point Hc and the line c, construct a line hc (rule W10b);

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

    % NDG: lines a and hc are not parallel

    % DET: lines a and hc are not the same

animation
Construction in GCLC language

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