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Problem 382 from Wernick's corpus: Ma, Hc, Ta


Problem

Given a point Ma, a point Hc 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 Ma and the point Ta, construct a line a (rule W02);

    % DET: points Ma and Ta are not the same

  2. Using the point Hc and the point Ma, construct a circle k(Ma,B) (rule W06);

    % NDG: points Hc and Ma are not the same

  3. Using the circle k(Ma,B) and the line a, construct a point B and a point C (rule W04);

    % NDG: line a and circle k(Ma,B) intersect

  4. Using the point Hc and the point B, construct a line c (rule W02);

    % DET: points Hc and B are not the same

  5. Using the point B, the point C, the point Ta and the line a, construct a point T`a (rule W19);

    % NDG: points B and C are not the same points C and Ta are not the same points C and midpoint([B,Ta]) are not the same

  6. Using the point Ta and the point T`a, construct a circle k_over(Ta,T`a) (rule W09);

    % NDG: points Ta and T`a are not the same

  7. Using the circle k_over(Ta,T`a) and the line c, construct a point Awb and a point A (rule W04);

    % NDG: line c and circle k_over(Ta,T`a) intersect

 animation
Construction in GCLC language

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