-
1.
(2021·射阳模拟)
(阅读理解)设点
在矩形
内部,当点
到矩形的一条边的两个端点距离相等时,称点
为该边的“和谐点”.例如:如图1,矩形
中,若
,则称
为边
的“和谐点”.
(解题运用)已知,点
在矩形
内部,且
,
.
-
(1)
设
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
是边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的“和谐点”,则
▲ 边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的“和谐点”(填“是”或“不是”);连接
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmrow%3E%3Cmi%3E%E5%9B%9B%3C%2Fmi%3E%3Cmi%3E%E8%BE%B9%3C%2Fmi%3E%3Cmi%3E%E5%BD%A2%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E4%3C%2Fmn%3E%3Cmsub%3E%3Cmi%3ES%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E%E2%96%B3%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值.
-
-
(2)
若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
是边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的“和谐点”,连接
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,当
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E90%3C%2Fmn%3E%3Cmo%3E%C2%B0%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
时,求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的值;
-
-
(3)
如图2,若
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3C%2Fmath%3E)
是边
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的“和谐点”,连接
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
;
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmi%3ED%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
,求
![](//math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmi%3Etan%3C%2Fmi%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmtext%3EPAB%3C%2Fmtext%3E%3Cmo%3E%E2%8B%85%3C%2Fmo%3E%3Cmi%3Etan%3C%2Fmi%3E%3Cmo%3E%E2%88%A0%3C%2Fmo%3E%3Cmtext%3EPBA%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
的最大值.
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