Question

在Rt△ABC中,∠A=90°,AB=AC=4,点E为AC的中点,点F在底边BC上,且FE⊥BE,则△CEF的面积是（

Answer 1

过F作FD⊥AC于D

∵∠BEF＝90°,∴∠AEB＋∠DEF＝90°

又∠AEB＋∠ABE＝90°,∴∠DEF＝∠ABE

又∠EDF＝∠A＝90°,∴△DEF∽△ABE

∴DE/DF＝AB/AE＝2,∴DE＝2DF

∵∠CDF＝90°,∠C＝45°,∴CD＝DF

∴EC＝3DF,∴DF＝1/3EC＝1/6AC＝4/6=2/3

∴△CEF的面积＝1/2×EC×DF＝1/2×4/2×2/3＝1/6