20 12 Analysis of 25 Mathematics Test Questions in Guangzhou Senior High School Entrance Examination - Training Enrollment Network

20 12 Analysis of 25 Mathematics Test Questions in Guangzhou Senior High School Entrance Examination

Let GH=x, then BE=2x.

CE？ = 10? -(2x)？ = 100-4x？，CF？ =FH？ +CH？ =(5-x)？ +5? -x？ =50- 10x

CE？ -CF？ =50-4x？ + 10x

When x=- 10/2×(-4)=5/4, there is a maximum value, and FH=5-x= 15/4, and CH=√5? -(5/4)? =5√ 15/4

∴tan∠fcd=tan∠gfc=ch/fh=√ 15/3

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