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776 B
776 B
AE=CF,\angle ACF=\angle EAB,AB=AC\therefore \triangle CAF \cong \triangle AEB
\therefore \angle ABE=\angle CAF
开始导角：
\angle 1=\angle 2,\angle 1+\angle 3=60^{\circ}
\therefore \angle 2+\angle 3=60^{\circ}
\therefore \angle APB=120^{\circ}
同时知道，此时AB=6
\therefore符合定角定弦规则，画出外接圆，设圆心为O
连接 OA,OB,OC
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。
同时可以证明\triangle AOC是直角三角形，且\angle OCA=30^{\circ}
可求CP=3\sqrt{3}