在三角形ABC中,角A,B,C的对边分别为a,b,c,c^2-b^2=ab,证明角C=角2B
在三角形ABC中,角A,B,C的对边分别为a,b,c,c^2-b^2=ab,证明角C=角2B
数学人气:573 ℃时间:2020-04-06 05:50:04
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延长AC至E使CE=BC=a 则∠ACB=2∠E----------①,c²-b²=ab c²=b(a+b) c/(a+b)=b/c 也就是说AB/AE=AC/AB∵∠A是公共角 ∴△ABE∽△ACB则它们的对应角∠E=∠ABC 代入①中得∠ACB=2∠...
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