The pentagon has been surrounded!

Geometry Level 4

If the equation of any two diagonals of a regular pentagon belongs to the family of lines \(\left(1+2\lambda\right)y - \left(2+\lambda\right)x +\left(1-\lambda\right)=0\) (where \(\lambda\) is an arbitrary constant) and their lengths are equal to \(\sin 36^{\circ}\), then find the locus of the centre of circle circumscribing the given pentagon.

Details:

  • The triangles formed by the two diagonals have no side common.
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