Question

关于三角形的数学题.如图,在三角形ABC中,∠ABC的平分线与∠ACB的外角平分线交于点D,试判断∠A与∠D有何关系,并

Answer 1

∠D与∠A的关系是 ∠A =2∠D.

延长BC至E

∵CD是∠ACB的外角平分线,AD是∠ABC的平分线

∴∠DCE=1/2∠ACE,∠DBC=1/2∠ABC

∵∠DCE=∠DBC+∠D

∠ACE=∠ABC+∠A ①

∴ 1/2∠ACE=1/2∠ABC+∠D

∴ ∠ACE=∠ABC+2∠D ②

由①②得 ∠ABC+∠A =∠ABC+2∠D

∴∠A =2∠D