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Problem 208 from Wernick's corpus: C, O, I


Problem

Given a point C, a point O and a point I, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point C and the point I, construct a line sc (rule W02);

    % DET: points C and I are not the same

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

    % NDG: points C and O are not the same

  3. Using the circle k(O,C), the line sc, the point O and the point C, construct a point Nc (rule W05);

    % NDG: line sc and circle k(O,C) intersect

    % DET: points C and Nc must be different

  4. Using the point I and the point Nc, construct a circle k(Nc,B) (rule W06);

    % NDG: points I and Nc are not the same

  5. Using the circle k(O,C) and the circle k(Nc,B), construct a point A and a point B (rule W07);

    % NDG: circles k(O,C) and k(Nc,B) intersect

    % DET: circles k(O,C) and k(Nc,B) are not the same

animation
Construction in GCLC language

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