invalid

GH//AC
AD/BD=AC/GH
CE/BG=PE/BP=AE/BH
AD/BD CE/AE=AC/GH BG/BH
AD/BD CE/AE BF/CF=AC/GH BG/BH BF/CF
triangle AFC and triangle BFH similar
BF/CF=BH/AC
left side= =AC/GH BG/BH BF/CF=AC/GH BG/BH BH/AC =BG/GH <1
Only when the left side =1 the equation holds. Now it is clearly invalid.