Problem #WSP-5305

Problem

Consider the triangle \(BCD\), inscribed in a circle with center \(A\), the segments \(EF\), \(FG\), \(EG\) are tangent to the circle at the points \(C\), \(D\), \(B\) respectively. Prove that the Euler line of the triangle \(BCD\) passes through the center of the circle circumscribed around the triangle \(EFG\).