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Let A ( 1, 0 ) , B ( 6, 2 ) and ...

Let ` A ( 1, 0 ) , B ( 6, 2 ) ` and ` C (( 3 ) /(2), 6 ) ` be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas , then the length of the line segment PQ, where Q is the point ` ( - ( 7 ) /(6), - ( 1 ) /(3)) , ` is _________.

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