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Problem 238 from Connelly's corpus: Ea, H, Ta


Problem

Given a point Ea, a point H and a point Ta, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Ea and the point H, construct a point A (rule W01);

  2. Using the point Ea and the point H, construct a line ha (rule W02);

    % DET: points Ea and H are not the same

  3. Using the point Ta and the point A, construct a line sa (rule W02);

    % DET: points Ta and A are not the same

  4. Using the point Ta and the line ha, construct a line a (rule W10a);

  5. Using the line a and the line ha, construct a point Ha (rule W03);

    % NDG: lines a and ha are not parallel

    % DET: lines a and ha are not the same

  6. Using the point H and the point Ha, construct a line m(HHa) (rule W14);

    % DET: points H and Ha are not the same

  7. Using the point Ea, the point A, the point Ta, the line sa and the line ha, construct a line AO (rule W17);

    % NDG: points A and Ta are not the same points Ea and A are not the same

    % DET: points A and Ta are not the same

  8. Using the point Ea and the line AO, construct a line m(HbHc) (rule W16);

  9. Using the line m(HbHc) and the line a, construct a point Ma (rule W03);

    % NDG: lines m(HbHc) and a are not parallel

    % DET: lines m(HbHc) and a are not the same

  10. Using the point Ma and the point A, construct a point G (rule W01);

  11. Using the point H and the point G, construct a point N (rule W01);

  12. Using the point Ea and the point N, construct a circle k(N,Ma) (rule W06);

    % NDG: points Ea and N are not the same

  13. Using the circle k(N,Ma) and the line m(HHa), construct a point Eb and a point Ec (rule W04);

    % NDG: line m(HHa) and circle k(N,Ma) intersect

  14. Using the point Eb and the point H, construct a point B (rule W01);

  15. Using the point H and the point Ec, construct a point C (rule W01);

animation
Construction in GCLC language

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