Construction Is A Piece Of Cake, Right? (Part-2)

Akshat influenced by Anshuman and took an arbitrary \(\bigtriangleup ABC\) and started doing aimless constructions, the steps of which are given below-

(\(1\)) He extended \(AB\) to a point \(D\) such that \(AD=BC\).

(\(2\)) Then he constructed an \(\angle ECA\) which is equal to \(\angle ABC\) (\(E\) being any point lying on the opposite side of \(AD\)).

(\(3\)) He then joined \(BE\) and \(DC\) which meet each other at \(X\).

(\(4\)) Then he joined \(AX\) which intersects \(EC\) at \(F\).

(\(5\)) Next, he joined \(AE\) and drew parallel to it from \(F\) which meets \(AC\) at \(G\).

Akshat then wondered what \(BG\) could possibly be equal to?