# 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.

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