My 200 followers problem!

Geometry Level 5

In ΔABC\Delta ABC ,

(1)DEBC DE || BC such that ADB,AECA - D - B , A - E - C

(2)JGCA JG || CA such that BJC,BGAB - J - C , B - G - A

(3)FIAB FI || AB such that CFA,CIBC - F - A , C - I - B

DE,IF,GJDE , IF , GJ are concurrent at HH

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

Find [ABC][ABC]

Details:Details:

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

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

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