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[几何] 一道几何最值

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hbghlyj posted 2020-4-14 09:28 |Read mode
Last edited by hbghlyj 2020-4-15 09:32给定锐角α和线段a,b,四边形EFGH中(不一定凸),∠GEH=α,FG=a,FE=b,EG=EH,
(1)求∠FEH的取值范围.
(2)求FH的取值范围.
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original poster hbghlyj posted 2020-4-15 09:37
Last edited by hbghlyj 2020-4-15 18:17(1)若a>b,0<∠FEH<180°
若a=b,0<∠FEH<90°+α
若a<b,$α\le\arcsin\frac ab,$则$0<∠FEH\le\arcsin\frac ab$
若a<b,$α>\arcsin\frac ab,$则$α-\arcsin\frac ab\le∠FEH\le\arcsin\frac ab$
(2)$\left|a-2b\sin\frac\alpha2\right|\le FH\le a+2b\sin\frac\alpha2$

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kuing posted 2020-4-15 14:26

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original poster hbghlyj posted 2020-4-15 18:20
回复 3# kuing
请看2#是否正确?

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