My 200 followers problem!

Geometry Level 5

In \(\Delta ABC\) ,

(1)\( DE || BC \) such that \(A - D - B , A - E - C\)

(2)\( JG || CA \) such that \(B - J - C , B - G - A\)

(3)\( FI || AB \) such that \(C - F - A , C - I - B\)

\(DE , IF , GJ\) are concurrent at \(H\)

Given that \([GDH] = 200 , [FHE] = 50 , [HIJ] = 450\) ,

Find \([ABC]\)

\(Details:\)

\((i)\) : \([ABC]\) represents area of \(\Delta ABC\)

\((iii)\) : \(A - D - B\) represents the betweeness property which means \(D\) is between \(A , B\)

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