Question

如图,在RT△ABC中,∠A=90°,AB=AC=8根号6,点E为AC中点,点F在底边BC上,且BE⊥FE,则△CEF的

Answer 1

AE=AC/2=4√6

BE^=AB^+AE^ => BE=4√30

tan∠ABE=AE/AB=1/2

tan∠ABC=AC/AB=1

tan∠EBF=tan(∠ABC-∠ABE)

=(tan∠ABC-tan∠ABE)/(1+tan∠ABC*tan∠ABE)

=1/3

EF=BE*tan∠EBF=4√30/3

S△ABC=AB*AC/2=192

S△ABE=AB*AE/2=86

S△BEF=BE*EF/2=80

S△CEF=S△ABC-S△ABE-S△BEF=6