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Problem 353 from Wernick's corpus: Ma, Mc, Hb


Problem

Given a point Ma, a point Mc and a point Hb, 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 Ma, construct a circle k(Ma,B) (rule W06);

    % NDG: points Hb and Ma are not the same

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

    % NDG: points Hb and Mc are not the same

  3. Using the circle k(Ma,B), the circle k(Mc,A), the point Hb, the point Ma and the point Mc, construct a point B (rule W08);

    % NDG: circles k(Ma,B) and k(Mc,A) intersect

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

animation
Construction in GCLC language

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