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Problem 238 from Wernick's corpus: C, Mc, I


Problem

Given a point C, a point Mc 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 Mc and the point I, construct a line IMc (rule W02);

    % DET: points Mc and I are not the same

  2. Using the point I and the point Mc, construct a circle k_over(I,Mc) (rule W09);

    % NDG: points I and Mc are not the same

  3. Using the point C and the line IMc, construct a line CP`c (rule W16);

  4. Using the point Mc, the line CP`c and the point C, construct a line hMc,-1/1(CP`c) (rule W15);

  5. Using the circle k_over(I,Mc) and the line hMc,-1/1(CP`c), construct a point Cfo and a point Pc (rule W04);

    % NDG: line hMc,-1/1(CP`c) and circle k_over(I,Mc) intersect

  6. Using the point Pc and the point I, construct a circle k(I,Pa) (rule W06);

    % NDG: points Pc and I are not the same

  7. Using the circle k(I,Pa), the point C and the point I, construct a line a and a line b (rule W12);

    % NDG: point C is outside the circle k(I,Pa)

  8. Using the circle k(I,Pa), the point Mc and the point I, construct a line x3 and a line c (rule W12);

    % NDG: point Mc is outside the circle k(I,Pa)

  9. Using the line a and the line c, construct a point B (rule W03);

    % NDG: lines a and c are not parallel

    % DET: lines a and c are not the same

  10. Using the point Mc and the point B, construct a point A (rule W01);

animation
Construction in GCLC language

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