Let \[\left(5, \frac{a}{4}\right)\] be the circumcenter of a triangle with vertices \[\mathrm{A}(a,-2), \mathrm{B}(a, 6)\] and \[C\left(\frac{a}{4},-2\right)\]. Let \[\alpha\] denote the circumradius, \[\beta\] denote the area and \[\gamma\] denote the perimeter of the triangle. Then \[\alpha+\beta+\gamma\] is