Properties of Triangle: JEE Main 2024 Mathematics question

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