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Problem 345 from Wernick's corpus: Ma, Mb, Hc


Problem

Given a point Ma, a point Mb 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 Hc and the point Ma, construct a circle k(Ma,B) (rule W06);

    % NDG: points Hc and Ma are not the same

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

    % NDG: points Hc and Mb are not the same

  3. Using the circle k(Ma,B), the circle k(Mb,C), the point Hc, the point Ma and the point Mb, construct a point C (rule W08);

    % NDG: circles k(Ma,B) and k(Mb,C) intersect

    % DET: circles k(Ma,B) and k(Mb,C) are not the same 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 Mb and the point C, construct a point A (rule W01);

animation
Construction in GCLC language

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