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Problem 493 from Wernick's corpus: G, Hc, Tc


Problem

Given a point G, a point Hc and a point Tc, 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 Tc, construct a line c (rule W02);

    % DET: points Hc and Tc are not the same

  2. Using the point Hc and the line c, construct a line hc (rule W10b);

  3. Using the point G, the line c and the point Hc, construct a line hG,-2/1(c) (rule W15);

  4. Using the line hG,-2/1(c) and the line hc, construct a point C (rule W03);

    % NDG: lines hG,-2/1(c) and hc are not parallel

    % DET: lines hG,-2/1(c) and hc are not the same

  5. Using the point C and the point G, construct a point Mc (rule W01);

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

    % DET: points Tc and C are not the same

  7. Using the point Mc and the line c, construct a line mc (rule W10b);

  8. Using the line mc and the line sc, construct a point Nc (rule W03);

    % NDG: lines mc and sc are not parallel

    % DET: lines mc and sc are not the same

  9. Using the point C and the point Nc, construct a line m(CNc) (rule W14);

    % DET: points C and Nc are not the same

  10. Using the line m(CNc) and the line mc, construct a point O (rule W03);

    % NDG: lines m(CNc) and mc are not parallel

    % DET: lines m(CNc) and mc are not the same

  11. 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

  12. Using the circle k(O,C) and the line c, construct a point A and a point B (rule W04);

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

animation
Construction in GCLC language

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