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XY is a line parallel to side BC of a t...

XY is a line parallel to side BC of a triangle ABC. If `B E\ ||\ A C`and `C F\ ||\ A B`meet XY at E and F respectively, show that `a r\ (A B E)\ =\ a r\ (A C F)`

Text Solution

Verified by Experts

From diagram we can see that
`ar(EBCY)=ar(BXFC)`
`ar(/_AEB)=1/2ar(EBLY)`
`arBXFC=2ar(/_AFC)`
from both the equations
ar(/_AEB)=ar(/_AFC)
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