# Construction Is A Piece Of Cake, Right?

**Geometry**Level 4

Anshuman took an arbitrary triangle \(ABC\) and started doing aimless constructions, the steps of which are given below:

(\(1\)) Through points \( A \) and \( B \), he drew two lines perpendicular to segment \( AB \). He extended \(BC\) where it intersected with the perpendicular at \(D\) and chose an arbitrary point \(F\) on perpendicular drawn from \(B\).

(\(2\)) Then he cuts an arc equal to \(BD\) on \(AD\) taking centre \(D\), he names that point \(E\).

(\(3\)) Then he joins \(DF\) and \(EB\) and extend them up to the point of intersection \(X\).

(\(4\)) Then he joined \(A\) with \(X\) and name their intersection with \(BF\) as \(G\).

(\(5\)) Then he joined \(AF\) and drew a parallel to it from \(G\) which intersects \(AB\) at \(H\).

He wonders: "What \(AH\) possibly be equal to?"

**Disclaimer**: Image not drawn up to scale.