We have a convex quadrilateral $ABCD$ with $AB = BD = 8$ and $CD = DA = 6$. Let $P$ be on side $AB$ such that $DP$ is bisector of angle $\angle ADB$ and $Q$ on side $BC$ such that $DQ$ is bisector of angle $\angle CDB$. Determine the value of the radius of the circle that passes through the vertices of the triangle $DPQ$.