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Problem 489 from Connelly's corpus: Ec, Mc, O


Problem

Given a point Ec, a point Mc and a point O, construct the triangle ABC.

Status

ArgoTriCS says that the problem is solvable.

Illustration

Figure of construction

Solution


  1. Using the point Ec and the point Mc, construct a line m(HbHa) (rule W02);

    % DET: points Ec and Mc are not the same

  2. Using the point Mc and the point O, construct a line mc (rule W02);

    % DET: points Mc and O are not the same

  3. Using the point Mc and the line mc, construct a line c (rule W10a);

  4. Using the point Ec and the point Mc, construct a line m(EcMc) (rule W14);

    % DET: points Ec and Mc are not the same

  5. Using the line m(EcMc) and the line m(HbHa), construct a point N (rule W03);

    % NDG: lines m(EcMc) and m(HbHa) are not parallel

    % DET: lines m(EcMc) and m(HbHa) are not the same

  6. Using the point N and the point O, construct a point G (rule W01);

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

  8. 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

  9. 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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