Question

如图,已知△ABC,CH⊥AB于H,点D在AC延长线上,若∠BCD=3∠A,求证：AH=BC+BH

Answer 1

延长AB到E使BE=BC ∴∠E=∠BCE ∵∠ABC=∠E+∠BCE ∴∠ABC=2∠E ∵∠BCD=3∠A ∠BCD=∠A+∠ABC ∴∠ABC=2∠A ∴∠A=∠E ∴AC=CE ∴CH⊥AB ∴AH=EH ∵EH=BE+BH=BH+BC ∴AH=BC+BH