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…

Let $\displaystyle \mathrm{A}(1,0), \mathrm{B}(6,2)$ and $\displaystyle \mathrm{C}\left(\frac{3}{2}, 6\right)$ 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 $\displaystyle \left(-\frac{7}{6},-\frac{1}{3}\right)$, is \_\_\_\_.