J. W. Fickett's problem for isosceles triangles

Two congruent overlapping isosceles triangles with the least angle between lateral sides are considered in the Euclidean plane. J. W. Fickett offered a bilateral estimation for the relation of the length of the part of the first triangle's boundary in the second triangle to the length of the part of the second triangle's the boundary in the first triangle. The paper shows that J. W. Fickett's supposition is not true in general. An analog of J. W. Fickett's estimation is proved for the isosceles triangles with the least angle between lateral sides.