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19 lines
776 B
19 lines
776 B
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- $AE=CF,\angle ACF=\angle EAB,AB=AC$
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$\therefore \triangle CAF \cong \triangle AEB$
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$\therefore \angle ABE=\angle CAF$
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开始导角：
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$\angle 1=\angle 2,\angle 1+\angle 3=60^{\circ}$
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$\therefore \angle 2+\angle 3=60^{\circ}$
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$\therefore \angle APB=120^{\circ}$
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同时知道，此时$AB=6$
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$\therefore$符合定角定弦规则，画出外接圆，设圆心为$O$
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连接 $OA,OB,OC$
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因为$\angle APB$一直等于$120^{\circ}$,所以$P$的轨迹一定是按圆的轨迹来运动，当$P$运动到$O,P,C$三点共线时，$CP$最短。
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同时可以证明$\triangle AOC$是直角三角形，且$\angle OCA=30^{\circ}$
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可求$CP=3\sqrt{3}$ |