抦傠偆両榓嶼偺悽奅両

嶼妟偵僠儍儗儞僕乮夝摎曇乯

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乕栤戣4乕

捈宎偑AB=2R偺墌偵丄拞怱傪A偲B偲偟偰敿宎偑R偺墌屖傪堷偔丅偦偟偰敿宎R/俀偺擇偮偺戝墌乮偁偍怓乯丄敿宎倲偺巐偮偺彫墌乮僆儗儞僕怓乯丄敿宎t乫偺巐偮偺彫墌乮偒傒偳傝怓乯偱側傞10屄偺墌偑恾偺傛偆偵愙偟偰偄傞丅偙偺帪t=t'=$\frac{R}{6}$傪妋偐傔傞丅
夝朄

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恾1-1

傑偢丄恾1-1偺傛偆偵B偲敿宎倲偺彫墌乮僆儗儞僕乯偺拞怱偲敿宎$\frac{俼}{俀}$偺戝墌乮偁偍乯偺拞怱傪寢傇偲捈妏嶰妏宍偑偱偒傞偺偱丄嶰暯曽偺掕棟偑棙梡偱偒傞丅
傛偭偰丄 \begin{align*} (R-t)^2=& (t+\frac{R}{2})^2+\frac{R}{2} ^2\\ R^2-2Rt+t^2=& t^2+Rt+\frac{R}{2}^2\\ t=& \frac{R}{6}\\ \end{align*}
師偵丄恾偺傛偆偵A偲敿宎t乫偺彫墌乮偒傒偳傝乯偺拞怱偲敿宎R偺戝墌乮偒乯偺拞怱傪寢傫偩嶰妏宍傪峫偊丄恾偺傛偆偵$\theta$傪偍偔丅

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恾1-2

嶰妏娭悢偺惈幙傛傝
\begin{align*} \cos{\theta}=\frac{t'}{R-t'} \end{align*} 傑偨丄恾偺嶰妏宍偵梋尫掕棟傪梡偄傞偲 \begin{align*} (R+t')^2=& (R-t')^2+R^2-2R(R-t')\cos{\theta}\\ =& (R-t')^2 + R^2 -2Rt'\\ R^2=& 6Rt'\\ t'=& \frac{1}{6}R\\ \end{align*}
仸峕屗帪戙偺恖偼嶰妏娭悢傪峫偊偢偵弶傔偐傜忋偺擇斣栚偺幃傪峫偊偰偄偨偦偆偱偡両

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