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王守恩 发表于 2019-9-1 04:25
在ΔADE 中,DE=sin20,AE=AD=sin80,FA=FE=sin80/2
在ΔABE 中,AE=sin60sin80/sin60,BE=sin40sin80 ...
在ΔABE 中:
∠GAE=20,∠GBA=60-B,∠GEB=E,
∠GAB=20,∠GBE=B, ∠GEA=80-E
正弦定理:
sin(20)sin(60-B)sin(E)/(sin(20)sin(B)sin(80-E))=1 (1)
角平分线定理:
sin(60-B)sin(80)/(sin(B)sin(40))=1 (2)
(2)代入(1):
sin(20)sin(40)sin(E)/(sin(20)sin(80)sin(80-E))=1
得E=50° 由50°=∠DEG=∠DGE,知DE=DG |
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