在三角形ABC中,角ACB=90度,CD垂直AB于D,E是BC中点,DE和AC的延长线交于F.试证明AC/BC=FA/FD

Question

在三角形ABC中,角ACB=90度,CD垂直AB于D,E是BC中点,DE和AC的延长线交于F.试证明AC/BC=FA/FD

Answer 1

证明：∵∠ACB = ∠BDC = 90°∴∠A = ∠ACB-∠B = 90°- ∠B, ∠BCD = ∠BDC-∠B = 90°- ∠B即,∠A = ∠BCD 且有∠B为公共角,∴△ACD∽△CBD∴AC/BC = AD/CD又∵E为BC中点,∠BDC=90°∴点E是RT三角形外接圆的圆心...