USAMO 2009/1 #29
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wangjiezhe
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USAMO 2009/1
#29
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设圆$\omega_1$ 和 $\omega_2$ 交于点 $X$ 、$Y$ ．过 $\omega_1$ 的圆心的直线 $l_1$ 交圆 $\omega_2$ 于点 $P$ 、$Q$ ，过 $\omega_2$ 的圆心的直线 $l_2$ 交 $\omega_1$ 于点 $R$ 、$S$ ．证明：若 $P$ 、$Q$ 、$R$ 、$S$ 四点共圆，则该圆心在直线 $XY$ 上．
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