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Problem 39 from Wernick's corpus: A, O, I


Problem

Given a point A, 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 A and the point I, construct a line sa (rule W02);

    % DET: points A and I are not the same

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

    % NDG: points A and O are not the same

  3. Using the circle k(O,C), the line sa, the point O and the point A, construct a point Na (rule W05);

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

    % DET: points A and Na must be different

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

    % NDG: points I and Na are not the same

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

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

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

animation
Construction in GCLC language

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