Straight Lines and Pair of Straight Lines Part 1

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 _____ .