Properties Of Triangle

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